%5E2%3D64.jpeg "(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:
- Add 5 to both sides: 4x = 13
- Divide both sides by 4: x = 13/4
Solving Equation 2:
- Add 5 to both sides: 4x = -3
- 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.