%5E2%3D25-solution-steps.jpeg "(x-5)^2=25 Solution Steps")
Solving the Equation (x-5)^2 = 25
This equation involves a squared term, which requires us to use the square root property to solve for x. Here are the steps:
1. Take the square root of both sides.
Remember that when we take the square root of both sides, we need to consider both positive and negative roots:
√((x-5)^2) = ±√25
2. Simplify the equation.
The square root of (x-5)^2 is simply (x-5) and the square root of 25 is 5. So the equation becomes:
x - 5 = ±5
3. Isolate x.
To isolate x, we add 5 to both sides of the equation:
x = 5 ± 5
4. Solve for both possible values of x.
- x = 5 + 5 = 10
- x = 5 - 5 = 0
Therefore, the solutions to the equation (x-5)^2 = 25 are x = 10 and x = 0.