Question

solve the equation by the square root property.
$(x - 8)^2 = 25$
what is the solution set?
(use a comma to separate answers as needed.)

Explanation:

Step1: Apply square root property

Take square roots of both sides:
$$\sqrt{(x-8)^2} = \pm\sqrt{25}$$
Simplify to get:
$$x-8 = \pm5$$

Step2: Solve for x (positive case)

Isolate x using +5:
$$x = 8 + 5$$
$$x = 13$$

Step3: Solve for x (negative case)

Isolate x using -5:
$$x = 8 - 5$$
$$x = 3$$

Answer:

$\{3, 13\}$