(x-7)^2=16 Square Root Method

2 min read Jun 17, 2024

Solving (x-7)² = 16 using the Square Root Method

This article will guide you through solving the equation (x-7)² = 16 using the square root method.

Understanding the Square Root Method

The square root method is a simple and effective way to solve equations that involve a squared term. The core idea is to isolate the squared term, take the square root of both sides, and then solve for the unknown variable.

Steps to Solve (x-7)² = 16

Isolate the squared term: The squared term is already isolated on the left side of the equation.
Take the square root of both sides: This eliminates the square on the left side. Remember that taking the square root can result in both positive and negative solutions.

√(x-7)² = ±√16
Simplify:
x - 7 = ±4
Solve for x: x = 7 ± 4
Find the two possible solutions:
- x = 7 + 4 = 11
- x = 7 - 4 = 3

Solution

Therefore, the solutions to the equation (x-7)² = 16 are x = 11 and x = 3.

Verification

You can verify your solutions by substituting them back into the original equation.

For x = 11: (11-7)² = 4² = 16 (This confirms the solution)
For x = 3: (3-7)² = (-4)² = 16 (This confirms the solution)

Conclusion

The square root method provides a straightforward approach to solving equations with squared terms. By understanding the steps and considering both positive and negative solutions, you can effectively find the solutions to such equations.