%5E2%3D81.jpeg "(2x-1)^2=81")
Solving the Equation (2x - 1)² = 81
This equation involves a squared term, which requires a specific approach to solve. Here's how to find the solutions for x:
1. Take the Square Root of Both Sides
Begin by taking the square root of both sides of the equation. Remember that taking the square root can result in both positive and negative values.
√[(2x - 1)²] = ±√81
2. Simplify
Simplify both sides of the equation.
2x - 1 = ±9
3. Solve for x
Now we have two separate equations to solve:
- Equation 1: 2x - 1 = 9
- Equation 2: 2x - 1 = -9
Solving Equation 1:
- Add 1 to both sides: 2x = 10
- Divide both sides by 2: x = 5
Solving Equation 2:
- Add 1 to both sides: 2x = -8
- Divide both sides by 2: x = -4
Therefore, the solutions for the equation (2x - 1)² = 81 are x = 5 and x = -4.
Checking the Solutions
To ensure our solutions are correct, let's substitute them back into the original equation:
For x = 5:
(2 * 5 - 1)² = (10 - 1)² = 9² = 81 (Correct!)
For x = -4:
(2 * -4 - 1)² = (-8 - 1)² = (-9)² = 81 (Correct!)
Conclusion
We have successfully solved the equation (2x - 1)² = 81 and found the solutions to be x = 5 and x = -4.