Question

(x-3)^2 - 25 = 0

Explanation:

Step1: Isolate the squared term

Add 25 to both sides of the equation:
$$(x - 3)^2 - 25 + 25 = 0 + 25$$
Simplify to get:
$$(x - 3)^2 = 25$$

Step2: Take square roots

Take the square root of both sides. Remember, a square root has two solutions (positive and negative):
$$x - 3 = \pm\sqrt{25}$$
Since $\sqrt{25} = 5$, this becomes:
$$x - 3 = \pm5$$

Step3: Solve for \( x \)

Case 1: \( x - 3 = 5 \)
Add 3 to both sides:
$$x = 5 + 3 = 8$$

Case 2: \( x - 3 = -5 \)
Add 3 to both sides:
$$x = -5 + 3 = -2$$

Answer:

\( x = 8 \) or \( x = -2 \)