2%3D81-responses.jpeg "(2 X−1)2=81 Responses")
Solving the Equation: (2x - 1)² = 81
This equation involves a squared term, so we'll need to use the square root property to solve for x. Let's break down the steps:
1. Take the Square Root of Both Sides
To get rid of the square, take the square root of both sides of the equation:
√[(2x - 1)²] = ±√81
This gives us:
2x - 1 = ±9
2. Solve for Two Possible Cases
We have two possible cases because the square root of 81 can be either positive or negative 9:
Case 1: 2x - 1 = 9 Case 2: 2x - 1 = -9
3. Solve for x in Each Case
Case 1:
- Add 1 to both sides: 2x = 10
- Divide both sides by 2: x = 5
Case 2:
- Add 1 to both sides: 2x = -8
- Divide both sides by 2: x = -4
Solution
Therefore, the solutions to the equation (2x - 1)² = 81 are x = 5 and x = -4.