(x+5)^2=81

2 min read Jun 17, 2024

Solving the Equation (x+5)^2 = 81

This equation involves a squared term, which requires us to carefully consider both positive and negative solutions. Let's break down the steps to solve it:

1. Isolate the Squared Term

Begin by isolating the squared term by taking the square root of both sides of the equation:

√((x+5)²) = ±√81

This simplifies to:

x + 5 = ±9

2. Solve for x

Now we have two separate equations to solve:

x + 5 = 9 Subtracting 5 from both sides, we get: x = 4
x + 5 = -9 Subtracting 5 from both sides, we get: x = -14

3. Verify the Solutions

It's always a good practice to substitute our solutions back into the original equation to verify they are correct:

For x = 4: (4 + 5)² = 9² = 81. This solution checks out.
For x = -14: (-14 + 5)² = (-9)² = 81. This solution also checks out.

Conclusion

Therefore, the solutions to the equation (x+5)² = 81 are x = 4 and x = -14.