Question

solve the equation by the square root property.
$(x - 1)^2 = 36$
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:
$$\sqrt{(x-1)^2} = \pm\sqrt{36}$$
Simplify to get:
$$x-1 = \pm 6$$

Step2: Solve for x (positive case)

Isolate x by adding 1 to both sides:
$$x = 6 + 1$$
$$x = 7$$

Step3: Solve for x (negative case)

Isolate x by adding 1 to both sides:
$$x = -6 + 1$$
$$x = -5$$

Answer:

$\{-5, 7\}$