%5E2%3D25.jpeg "(2x-7)^2=25")
Solving the Equation: (2x-7)^2 = 25
This equation involves a squared term, which we can solve using the following steps:
1. Take the Square Root of Both Sides
The first step is to get rid of the square on the left side of the equation. We do this by taking the square root of both sides:
√[(2x-7)^2] = ±√25
This gives us:
2x - 7 = ±5
2. Solve for Two Possible Values
Now we have two separate equations to solve:
Equation 1: 2x - 7 = 5
Equation 2: 2x - 7 = -5
3. Solve for 'x' in Each Equation
For Equation 1:
- Add 7 to both sides: 2x = 12
- Divide both sides by 2: x = 6
For Equation 2:
- Add 7 to both sides: 2x = 2
- Divide both sides by 2: x = 1
4. The Solutions
Therefore, the solutions to the equation (2x-7)^2 = 25 are:
- x = 6
- x = 1