Solve by completing the square.
-$$x ^ { 2 } = - 4 x + 9$$
A) $\frac { 4 + 2 \sqrt { 13 } } { 2 }$
B) $\frac { - 4 \pm 2 \sqrt { 13 } } { 2 }$
C) $\frac { - 4 - 2 \sqrt { 13 } } { 2 }$
D) $- 4 \pm 2 \sqrt { 13 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 = -4x + 9$ by completing the square, first move all terms to one side to get $x^2 + 4x - 9 = 0$. Then, add $(\frac{4}{2})^2 = 4$ to both sides to complete the square: $x^2 + 4x + 4 = 13$. This gives $(x + 2)^2 = 13$, so $x + 2 = \pm \sqrt{13}$, leading to $x = -2 \pm \sqrt{13}$. Simplifying gives $x = \frac{-4 \pm 2\sqrt{13}}{2}$, which matches choice B.

Solve by Completing the Square x2=−4x+9x ^ { 2 } = - 4 x + 9x2=−4x+9

Solve by Completing the Square $x ^ { 2 } = - 4 x + 9$