Question

now, write $x^2 - 16x + 64 = -8$ as \checkmark $(x - 8)^2 = -8$ \complete take the square root of both sides to get the solutions \boxed{} \pm \boxed{} $\sqrt{2}i$

Explanation:

Step1: Isolate squared binomial

We start with the given completed square form:
$$(x - 8)^2 = -8$$

Step2: Take square roots of both sides

Apply square root property, recall $\sqrt{-1}=i$:
$$x - 8 = \pm\sqrt{-8} = \pm\sqrt{4\times2\times(-1)} = \pm2\sqrt{2}i$$

Step3: Solve for x

Isolate x by adding 8 to both sides:
$$x = 8 \pm 2\sqrt{2}i$$

Answer:

$8$ $\pm$ $2$ $\sqrt{2}i$