(x+2)^2=9

2 min read Jun 16, 2024

Solving the Equation (x+2)^2 = 9

This article will guide you through the steps of solving the equation (x+2)^2 = 9.

Understanding the Equation

The equation involves a squared term, (x+2)^2, which represents the square of the expression (x+2). We aim to find the value(s) of 'x' that satisfy this equation.

Solving for x

Take the square root of both sides: √[(x+2)^2] = ±√9
Simplify: x + 2 = ±3
Solve for two possible cases:

Case 1: x + 2 = 3 x = 3 - 2 x = 1

Case 2: x + 2 = -3 x = -3 - 2 x = -5

Solutions

Therefore, the solutions to the equation (x+2)^2 = 9 are x = 1 and x = -5.

Verification

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

For x = 1: (1 + 2)^2 = 3^2 = 9 (True)
For x = -5: (-5 + 2)^2 = (-3)^2 = 9 (True)

Conclusion

We have successfully solved the equation (x+2)^2 = 9 by using the square root property. The solutions are x = 1 and x = -5. Remember to always consider both positive and negative square roots when solving equations involving squares.