Solve Quadratic Equations by Completing the Square
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } - \frac { 2 } { 7 } x$$
A) $\frac { 1 } { 49 } ; x ^ { 2 } - \frac { 2 } { 7 } x + \frac { 1 } { 49 } = \left( x - \frac { 1 } { 7 } \right) ^ { 2 }$
B) $\frac { 1 } { 49 } ; x ^ { 2 } - \frac { 2 } { 7 } x + \frac { 1 } { 49 } = \left( x + \frac { 1 } { 7 } \right) ^ { 2 }$
C) $\frac { 4 } { 49 } ; x ^ { 2 } - \frac { 2 } { 7 } x + \frac { 4 } { 49 } = \left( x - \frac { 2 } { 7 } \right) ^ { 2 }$
D) $\frac { 2 } { 49 } ; x ^ { 2 } - \frac { 2 } { 7 } x + \frac { 2 } { 49 } = \left( x - \frac { 1 } { 7 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

To complete the square, we need to add $\left(\frac{-2/7}{2}\right)^2=\frac{1}{49}$ to the expression. Then we have 
$$x ^ { 2 } - \frac { 2 } { 7 } x +\frac{1}{49}= \left( x - \frac { 1 } { 7 } \right) ^ { 2 }$$ 
which is a perfect square trinomial. Therefore, the constant that should be added is $\frac{1}{49}$ and the factored form is $$\left( x - \frac { 1 } { 7 } \right) ^ { 2 }$$

Solve Quadratic Equations by Completing the Square Determine the Constant x2−27xx ^ { 2 } - \frac { 2 } { 7 } xx2−72​x

Solve Quadratic Equations by Completing the Square
Determine the Constant $x ^ { 2 } - \frac { 2 } { 7 } x$