(x-6)^2=9

2 min read Jun 17, 2024

Solving the Equation (x-6)^2 = 9

This article will guide you through solving the equation (x-6)^2 = 9. We will explore the steps involved in finding the solutions for x.

Understanding the Equation

The equation (x-6)^2 = 9 represents a quadratic equation. It involves a squared term, which means we have two possible solutions for x.

Solving the Equation

Take the square root of both sides: To get rid of the square, we take the square root of both sides of the equation. Remember that taking the square root introduces both positive and negative solutions.

√(x-6)^2 = ±√9
Simplify: Simplifying both sides gives us:

x - 6 = ±3
Isolate x: To find the values of x, we add 6 to both sides of the equation:

x = 6 ± 3
Calculate the solutions: This gives us two solutions:
- x = 6 + 3 = 9
- x = 6 - 3 = 3

Verifying the Solutions

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

For x = 9: (9 - 6)^2 = 3^2 = 9
For x = 3: (3 - 6)^2 = (-3)^2 = 9

Both solutions satisfy the original equation.

Conclusion

The solutions for the equation (x-6)^2 = 9 are x = 9 and x = 3. This demonstrates the process of solving quadratic equations with squared terms. By taking the square root of both sides and isolating x, we can find the two possible solutions.