%5E2%3D60-square-root-method.jpeg "(x-7)^2=60 Square Root Method")
Solving (x-7)^2 = 60 using the Square Root Method
The square root method is a simple and efficient way to solve equations in the form of (x - a)^2 = b. Let's break down how to solve the equation (x-7)^2 = 60 using this method.
1. Isolate the Squared Term
Our goal is to get the term with the square by itself. In this case, the squared term is already isolated:
(x - 7)^2 = 60
2. Take the Square Root of Both Sides
Take the square root of both sides of the equation to eliminate the square on the left side. Remember, when taking the square root, we need to consider both positive and negative solutions:
√((x - 7)^2) = ±√60
This simplifies to:
(x - 7) = ±√60
3. Simplify the Radical (If Possible)
We can simplify √60 by finding its prime factorization: √60 = √(2² * 3 * 5) = 2√15.
Therefore:
(x - 7) = ±2√15
4. Isolate x
To get x by itself, add 7 to both sides of the equation:
x = 7 ± 2√15
5. Solutions
This gives us two possible solutions:
- x = 7 + 2√15
- x = 7 - 2√15
These are the exact solutions to the equation (x - 7)^2 = 60. You can approximate them using a calculator if needed.
Summary
By following these steps, we successfully solved the equation (x - 7)^2 = 60 using the square root method. This method is a straightforward approach that allows us to efficiently find the solutions to equations in this form.