m%C5%A9-2%3D81.jpeg "(2x-1)mũ 2=81")
Solving the Equation (2x - 1)² = 81
This article will guide you through the steps of solving the equation (2x - 1)² = 81.
Understanding the Equation
The equation (2x - 1)² = 81 represents a quadratic equation. It involves a squared term, which means there will likely be two solutions.
Solving the Equation
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Take the square root of both sides: √(2x - 1)² = ±√81 2x - 1 = ±9
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Solve for two separate cases:
- Case 1: 2x - 1 = 9
- Add 1 to both sides: 2x = 10
- Divide both sides by 2: x = 5
- Case 2: 2x - 1 = -9
- Add 1 to both sides: 2x = -8
- Divide both sides by 2: x = -4
- Case 1: 2x - 1 = 9
Solution
Therefore, the solutions to the equation (2x - 1)² = 81 are x = 5 and x = -4.
Verification
You can verify these solutions by plugging them back into the original equation:
- For x = 5: (2(5) - 1)² = 9² = 81
- For x = -4: (2(-4) - 1)² = (-9)² = 81
Both solutions satisfy the original equation.