(x + 10)^2 - 25 = 36

Answer 1

To solve the equation \((x + 10)^2 - 25 = 36\), follow these steps:

1. First, isolate the squared term by adding 25 to both sides of the equation: \[ (x + 10)^2 - 25 + 25 = 36 + 25 \] Simplifying this gives: \[ (x + 10)^2 = 61 \]

2. Next, take the square root of both sides: \[ x + 10 = \pm \sqrt{61} \]

3. Now, solve for \(x\) by subtracting 10 from both sides: \[ x = -10 \pm \sqrt{61} \]

This gives us two possible solutions: \[ x = -10 + \sqrt{61} \quad \text{and} \quad x = -10 - \sqrt{61} \]

Thus, the solutions are: \[ x = -10 + \sqrt{61} \quad \text{and} \quad x = -10 - \sqrt{61} \]