Question

(X - 7) squared equals 11

Answer 1

To solve the equation \((X - 7)^2 = 11\), follow these steps:

1. Take the square root of both sides of the equation:
\[
X - 7 = \pm \sqrt{11}
\]

2. This gives us two separate equations to solve:
\[
X - 7 = \sqrt{11} \quad \text{and} \quad X - 7 = -\sqrt{11}
\]

3. Solve for \(X\) in both cases:
- For the first equation:
\[
X = 7 + \sqrt{11}
\]
- For the second equation:
\[
X = 7 - \sqrt{11}
\]

Therefore, the solutions for the equation \((X - 7)^2 = 11\) are:
\[
X = 7 + \sqrt{11} \quad \text{and} \quad X = 7 - \sqrt{11}
\]