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(4x-5)^2=64

2 min read Jun 16, 2024
(4x-5)^2=64

Solving the Equation (4x - 5)^2 = 64

This equation involves a squared term, so we need to use the square root property to solve it. Here's how to break it down:

Step 1: Isolate the Squared Term

The squared term is (4x - 5)^2. It's already isolated on one side of the equation, so we can proceed to the next step.

Step 2: Take the Square Root of Both Sides

Taking the square root of both sides gives us:

√(4x - 5)^2 = ±√64

This simplifies to:

4x - 5 = ±8

Step 3: Solve for x

Now we have two separate equations to solve:

  • Equation 1: 4x - 5 = 8
  • Equation 2: 4x - 5 = -8

Solving Equation 1:

  1. Add 5 to both sides: 4x = 13
  2. Divide both sides by 4: x = 13/4

Solving Equation 2:

  1. Add 5 to both sides: 4x = -3
  2. Divide both sides by 4: x = -3/4

Solution

Therefore, the solutions to the equation (4x - 5)^2 = 64 are x = 13/4 and x = -3/4.

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