(x-5)^2=25 Solution Steps

Jasonbradley

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Jun 17, 2024

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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.