Solve by completing the square.
-$$z ^ { 2 } + 4 z - 9 = 0$$
A) $- 2 \pm \sqrt { 13 }$
B) $- 1 \pm \sqrt { 13 }$
C) $- 2 \pm 2 \sqrt { 13 }$
D) $2 + \sqrt { 13 }$

Question

Quizplus · Accepted Answer

To solve the equation $z^2 + 4z - 9 = 0$ by completing the square, first move the constant term to the other side: $z^2 + 4z = 9$. Then, add the square of half the coefficient of $z$ to both sides: $(4/2)^2 = 4$. So, $z^2 + 4z + 4 = 9 + 4$, which simplifies to $(z + 2)^2 = 13$. Taking the square root of both sides gives $z + 2 = \pm \sqrt{13}$, so $z = -2 \pm \sqrt{13}$.

Solve by Completing the Square z2+4z−9=0z ^ { 2 } + 4 z - 9 = 0z2+4z−9=0

Solve by Completing the Square $z ^ { 2 } + 4 z - 9 = 0$