(x+1)^2=81

2 min read Jun 16, 2024

Solving the Equation (x+1)^2 = 81

This article will guide you through the steps of solving the equation (x+1)^2 = 81.

Understanding the Equation

The equation represents a quadratic equation, which means it involves a variable raised to the power of two. To solve it, we need to isolate the variable x.

Steps to Solve

Take the square root of both sides:
- √((x+1)^2) = ±√81
- This gives us: x+1 = ±9
Solve for two possible values of x:
- Case 1: x+1 = 9
  - Subtract 1 from both sides: x = 8
- Case 2: x+1 = -9
  - Subtract 1 from both sides: x = -10

Solutions

Therefore, the solutions to the equation (x+1)^2 = 81 are x = 8 and x = -10.

Verification

We can verify our solutions by plugging them back into the original equation:

For x = 8:
- (8+1)^2 = 9^2 = 81
For x = -10:
- (-10+1)^2 = (-9)^2 = 81

Both solutions satisfy the original equation, confirming their validity.