(x-5)^2=25

2 min read Jun 17, 2024

Solving the Equation (x-5)^2 = 25

This equation involves a squared term, which requires a specific approach to solve for the unknown variable, 'x'. Here's a step-by-step breakdown:

1. Isolate the Squared Term

The first step is to get the squared term by itself on one side of the equation. Since the equation is already in this form, we can move on to the next step.

2. Take the Square Root of Both Sides

To eliminate the square, take the square root of both sides of the equation. Remember that when taking the square root, there are two possible solutions: a positive and a negative root.

√[(x-5)²] = ±√25

3. Simplify

Simplify both sides of the equation.

x - 5 = ±5

4. Solve for x

Isolate 'x' by adding 5 to both sides of the equation:

x = 5 ± 5

5. Find the Solutions

This gives us two possible solutions:

x = 5 + 5 = 10
x = 5 - 5 = 0

Conclusion

Therefore, the solutions to the equation (x-5)² = 25 are x = 10 and x = 0.