Question

solve the following quadratic equation by the square root method. if needed, write your answer as a fraction reduced to lowest terms.
$z^2 - 16z + 64 = -144$
$z = \boxed{}$ or $\boxed{}$

Explanation:

Step1: Rewrite left side as square

$z^2 - 16z + 64 = (z-8)^2$
Equation becomes: $(z-8)^2 = -144$

Step2: Take square roots of both sides

$z-8 = \pm\sqrt{-144}$
$\sqrt{-144} = \sqrt{144 \times (-1)} = 12i$

Step3: Solve for z

$z = 8 \pm 12i$

Answer:

$z = 8 + 12i$ or $z = 8 - 12i$