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
 Case 1: x+1 = 9
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.