(2x-5)^2=81

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (2x - 5)^2 = 81

This equation involves a squared term, making it a quadratic equation. Here's how to solve it:

1. Take the Square Root of Both Sides

To get rid of the square, we take the square root of both sides of the equation:

√((2x - 5)²) = ±√81

This gives us:

2x - 5 = ±9

2. Solve for Two Possible Cases

Now we have two separate equations to solve:

Case 1: 2x - 5 = 9

Case 2: 2x - 5 = -9

3. Solve for x in Each Case

Case 1:

• Add 5 to both sides: 2x = 14
• Divide both sides by 2: x = 7

Case 2:

• Add 5 to both sides: 2x = -4
• Divide both sides by 2: x = -2

4. Solutions

Therefore, the solutions to the equation (2x - 5)² = 81 are x = 7 and x = -2.