To solve the equation \((X - 4)^2 = 25\), we will first take the square root of both sides. 1. Taking the square root: \[ X - 4 = \pm 5 \] 2. This results in two cases: - Case 1: \[ X - 4 = 5 \] Adding 4 to both sides gives: \[ X = 9 \] - Case 2: \[ X - 4 = -5 \] Adding 4 to both sides gives: \[ X = -1 \] So the solutions to the equation \((X - 4)^2 = 25\) are: \[ X = 9 \quad \text{and} \quad X = -1 \]

(X-4)^2 = 25

1 answer

To solve the equation \((X - 4)^2 = 25\), we will first take the square root of both sides.

Taking the square root: \[ X - 4 = \pm 5 \]
This results in two cases:
- Case 1: \[ X - 4 = 5 \] Adding 4 to both sides gives: \[ X = 9 \]
- Case 2: \[ X - 4 = -5 \] Adding 4 to both sides gives: \[ X = -1 \]

So the solutions to the equation \((X - 4)^2 = 25\) are: \[ X = 9 \quad \text{and} \quad X = -1 \]