(x-7)^2=64 Square Root Method

Jasonbradley

2 min read

·

Jun 17, 2024

29

Share

Solving (x-7)^2 = 64 using the Square Root Method

This article will guide you through solving the equation (x-7)² = 64 using the square root method. This method provides a straightforward way to isolate the variable x.

Understanding the Square Root Method

The square root method relies on the principle that for any number a, the square root of a² is simply a. We can apply this principle to solve equations where a variable is squared.

Steps to Solve the Equation

1. Isolate the squared term: In this case, the squared term is already isolated: (x-7)² = 64.
2. Take the square root of both sides: Applying the square root to both sides gives us: √(x-7)² = ±√64.
3. Simplify: √(x-7)² simplifies to (x-7), and √64 equals 8. Therefore, we have: (x-7) = ±8.
4. Solve for x: Now we have two separate equations:
   • x - 7 = 8
   • x - 7 = -8
5. Solve for x in each equation:
   • x - 7 = 8 Adding 7 to both sides gives us x = 15.
   • x - 7 = -8 Adding 7 to both sides gives us x = -1.

Conclusion

By applying the square root method, we successfully solved the equation (x-7)² = 64, obtaining two solutions: x = 15 and x = -1. Remember to consider both positive and negative square roots when solving equations using this method.