%5E2%3D25.jpeg "(x-7)^2=25")
Solving the Equation (x-7)^2 = 25
This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's a step-by-step guide:
1. Isolate the squared term
The squared term is already isolated on the left side of the equation.
2. Take the square root of both sides
Remember that taking the square root of a number can result in both positive and negative solutions.
√[(x-7)²] = ±√25
3. Simplify
This simplifies to:
x - 7 = ±5
4. Solve for x
Now, we have two separate equations to solve:
- Equation 1: x - 7 = 5
- Equation 2: x - 7 = -5
Solving Equation 1:
- Add 7 to both sides: x = 12
Solving Equation 2:
- Add 7 to both sides: x = 2
5. The Solutions
Therefore, the solutions to the equation (x-7)² = 25 are x = 12 and x = 2.