Deck 10: Completing the Square
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Deck 10: Completing the Square
1
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

C
2
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

D
3
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

C
4
Suppose a deposit of $3,500 in a savings account that paid an annual interest rate
(compounded yearly) is worth $3,977 after 2 years. Using the formula
, we have
Solve for r to find the annual interest rate. Round the answer to the nearest tenth.
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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5
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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6
Fill in the blanks so that the left side of each is a perfect square trinomial; that is, complete the square.
_____
_____ 
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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7
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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8
In the figure below, triangle ABC has angles
and
and height k . Find the lengths of sides AB , BC , and AC , in terms of k . 
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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9
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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10
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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11
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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12
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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13
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 
A)
B)
C)
D)
E)



A)

B)

C)

D)

E)

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14
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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15
If the length of the shorter sides of a
triangle is
, find the length of the hypotenuse, in terms of
. 
A)
B)
C)
D)
E)




A)

B)

C)

D)

E)

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16
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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17
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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18
Solve the following quadratic equation by completing the square. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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19
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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20
Simplify. 
A) 7
B) 3
C) 1
D) 9
E) 5

A) 7
B) 3
C) 1
D) 9
E) 5
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21
Solve the following quadratic equation by completing the square.
a = __________

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22
Solve the equation using the quadratic formula. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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23
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 



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24
Simplify. 

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25
Solve the equation.
x = __________

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26
Solve the following quadratic equation by completing the square.
x = __________

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27
If the length of the shorter sides of a
triangle is x , find the length of the hypotenuse, in terms of x . 


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28
Solve the following quadratic equation by completing the square.
a = __________

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29
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 



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30
Solve the following quadratic equation by completing the square.
x = __________

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31
Solve the following quadratic equation by completing the square.
x = __________

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32
Solve the equation.
x = __________

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33
Solve the equation.
x = __________

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34
Solve the equation.
y = __________

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35
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 



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36
Solve the following quadratic equation by completing the square.
x = __________

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37
Solve the equation.
y = __________

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38
Suppose a deposit of $3,500 in a savings account that paid an annual interest rate r (compounded yearly) is worth $4,098 after 2 years. Using the formula
, we have
Solve for r to find the annual interest rate. Round the answer to the nearest tenth. r = __________%


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39
Solve the equation.
x = __________

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40
Fill in the blanks so that the left side is a perfect square trinomial; that is, complete the square.
_____
_____ 



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41
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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42
Solve the equation using the quadratic formula. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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43
Find the value of
when 


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44
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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Unlock for access to all 187 flashcards in this deck.
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k this deck
45
Writing in 1829, former President James Madison made some predictions about the growth of the population of the United States. The populations he predicted fit the equation
where y is the population in millions of people x years from 1829. Use the equation to determine the approximate year President Madison would have predicted that the U.S. population would reach 100,000,000. Round answer to the nearest year.
A) 1914
B) 1904
C) 1908
D) 1930
E) 1897

A) 1914
B) 1904
C) 1908
D) 1930
E) 1897
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46
The total cost (in dollars) for a company to manufacture and sell
items per week is
, whereas the revenue brought in by selling all
items is
. How many items must be sold to obtain a weekly profit of $500?
A) 40 or 80 items
B) 10 or 110 items
C) 50 items
D) 70 items
E) 70 or 80 items




A) 40 or 80 items
B) 10 or 110 items
C) 50 items
D) 70 items
E) 70 or 80 items
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47
Multiply both sides of the equation by their LCD. Then solve the resulting equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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48
An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance s it travels and time t is given by
. How long does it take the object to fall 70 feet?
A) 5 seconds
B) 3 seconds
C) 1 second
D) 2 seconds
E) 4 seconds

A) 5 seconds
B) 3 seconds
C) 1 second
D) 2 seconds
E) 4 seconds
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49
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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50
Writing in 1829, former President James Madison made some predictions about the growth of the population of the United States. The populations he predicted fit the equation
where y is the population in millions of people x years from 1829. Use the equation to determine the approximate year President Madison would have predicted that the U.S. population would reach 140,000,000. Round the answer to the nearest year.

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51
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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52
Look for the greatest common factor, then use the quadratic formula to find all solutions. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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53
Solve the equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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54
Look for the greatest common factor, then use the quadratic formula to find all solutions. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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55
An object is thrown downward with an initial velocity of 3 feet per second. The relationship between the distance s it travels and time t is given by
. How long does it take the object to fall 70 feet? __________ second(s)

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56
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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57
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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58
Multiply both sides of the equation by their LCD. Then solve the resulting equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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59
Find the value of
when 
A) 1
B) 196
C) - 196
D) - 164
E) 164


A) 1
B) 196
C) - 196
D) - 164
E) 164
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60
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.) 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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61
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
x = __________

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62
Multiply both sides of the equation by their LCD. Then solve the resulting equation.
r = __________

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63
Solve the equation using the quadratic formula.
x = __________

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64
Look for the greatest common factor, then use the quadratic formula to find all solutions.
y = __________

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65
Use the discriminant to find the number and kind of solutions for the following equation. 
A)
B)
C)
D)
E)

A)

B)

C)

D)

E)

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66
Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = 30, two irrational
B) D = - 16, two complex
C) D = 24, two rational
D) D = 25, two rational
E) D = 0, one rational

A) D = 30, two irrational
B) D = - 16, two complex
C) D = 24, two rational
D) D = 25, two rational
E) D = 0, one rational
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67
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
r = __________

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k this deck
68
Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = 0, one rational
B) D = 30, two irrational
C) D = - 25, two complex
D) D = - 30, two complex
E) D = 25, two rational

A) D = 0, one rational
B) D = 30, two irrational
C) D = - 25, two complex
D) D = - 30, two complex
E) D = 25, two rational
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69
Multiply both sides of the equation by their LCD. Then solve the resulting equation.
y = __________

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70
Solve the equation.
x = __________

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71
Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = - 9, two complex
B) D = 9, two rational
C) D = 0, one rational
D) D = 41, two irrational
E) D = - 41, two complex

A) D = - 9, two complex
B) D = 9, two rational
C) D = 0, one rational
D) D = 41, two irrational
E) D = - 41, two complex
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72
Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = -9, two complex
B) D = - 3, two complex
C) D = 0, one rational
D) D = 9, two rational
E) D = 3, two irrational

A) D = -9, two complex
B) D = - 3, two complex
C) D = 0, one rational
D) D = 9, two rational
E) D = 3, two irrational
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73
Look for the greatest common factor, then use the quadratic formula to find all solutions.
t = __________

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74
Use the discriminant to find the number and kind of solutions for the following equation. 
A) D = - 9, two complex
B) D = 9, two rational
C) D = - 13, two complex
D) D = 0, one rational
E) D = 13, two irrational

A) D = - 9, two complex
B) D = 9, two rational
C) D = - 13, two complex
D) D = 0, one rational
E) D = 13, two irrational
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75
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
x = __________

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76
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
x = __________

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77
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
x = __________

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78
The total cost (in dollars) for a company to manufacture and sell x items per week is
, whereas the revenue brought in by selling all x items is
. How many items must be sold to obtain a weekly profit of $300? __________ items


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79
Solve the equation.
t = __________

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80
Solve the equation. Use factoring or the quadratic formula, whichever is appropriate. (Try factoring first. If you have any difficulty factoring, then go right to the quadratic formula.)
x = __________

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