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(2x-1)mũ 2=81

2 min read Jun 16, 2024
(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

  1. Take the square root of both sides: √(2x - 1)² = ±√81 2x - 1 = ±9

  2. 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

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.

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