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(4x-5)^2=9

2 min read Jun 16, 2024
(4x-5)^2=9

Solving the Equation: (4x-5)^2 = 9

This equation involves a squared term, which often calls for a specific approach to solve. Let's break down the steps:

1. Isolate the Squared Term

  • First, we need to isolate the term (4x-5)² on one side of the equation. Since the equation already has this term isolated, we can proceed to the next step.

2. Take the Square Root of Both Sides

  • Taking the square root of both sides will eliminate the square and give us:

    √((4x-5)²) = ±√9

  • Simplifying this:

    4x - 5 = ±3

3. Solve for x

  • Now we have two separate equations to solve:

    Equation 1: 4x - 5 = 3

    • Add 5 to both sides: 4x = 8
    • Divide both sides by 4: x = 2

    Equation 2: 4x - 5 = -3

    • Add 5 to both sides: 4x = 2
    • Divide both sides by 4: x = 1/2

4. Solution

Therefore, the solutions to the equation (4x-5)² = 9 are x = 2 and x = 1/2.

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