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.
-$$x ^ { 2 } - 3 x$$
A) $\frac { 9 } { 4 } ; x ^ { 2 } - 3 x + \frac { 9 } { 4 } = \left( x - \frac { 3 } { 2 } \right) ^ { 2 }$
B) $- \frac { 9 } { 4 } ; x ^ { 2 } - 3 x - \frac { 9 } { 4 } = \left( x - \frac { 3 } { 2 } \right) ^ { 2 }$
C) $\frac { 3 } { 2 } ; x ^ { 2 } - 3 x + \frac { 3 } { 2 } = \left( x - \frac { 3 } { 2 } \right) ^ { 2 }$
D) $9 ; x ^ { 2 } - 3 x + 9 = ( x - 3 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

To complete the square, we need to add $\left(\frac{-b}{2a}\right)^2$ to the equation, where $b$ is the coefficient of $x$ and $a$ is the coefficient of $x^2$. In this case, $a=1$ and $b=-3$, so we need to add $\left(\frac{-(-3)}{2(1)}\right)^2=\frac{9}{4}$ to the equation. This gives us:
$$x^2-3x+\frac{9}{4}=\left(x-\frac{3}{2}\right)^2$$
The answer is A because it correctly identifies the constant that should be added and the completed square, which is a perfect square trinomial.

Solve Quadratic Equations by Completing the Square Determine the Constant x2−3xx ^ { 2 } - 3 xx2−3x

Solve Quadratic Equations by Completing the Square
Determine the Constant $x ^ { 2 } - 3 x$