(x-5)^2=25 Steps

2 min read Jun 17, 2024

Solving the Equation (x - 5)² = 25

This article will guide you through the steps to solve the equation (x - 5)² = 25. This type of equation involves a squared term, so we'll use the square root property to solve it.

Step 1: Take the Square Root of Both Sides

To eliminate the square on the left side, we take the square root of both sides of the equation:

√[(x - 5)²] = ±√25

Note: We use the ± sign because the square root of a number can be positive or negative.

Step 2: Simplify Both Sides

Simplifying the equation gives us:

x - 5 = ±5

Step 3: Isolate x

To get x by itself, we add 5 to both sides of the equation:

x = 5 ± 5

Step 4: Solve for the Two Possible Values of x

Now we have two possible solutions:

Solution 1: x = 5 + 5 = 10

Solution 2: x = 5 - 5 = 0

Conclusion

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