%5E2%3D9.jpeg "(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
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Taking the square root of both sides will eliminate the square and give us:
√((4x-5)²) = ±√9
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Simplifying this:
4x - 5 = ±3
3. Solve for x
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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.