2%3D81.jpeg "(2x−1)2=81")
Solving the Equation (2x-1)^2 = 81
This article will guide you through the steps involved in solving the equation (2x-1)^2 = 81.
Understanding the Equation
The equation presents a squared term, (2x-1)^2, which is equal to 81. To solve for x, we need to isolate it.
Solving the Equation
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Take the square root of both sides:
- √(2x-1)^2 = ±√81
- 2x-1 = ±9
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Solve for two possible cases:
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Case 1: 2x-1 = 9
- 2x = 10
- x = 5
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Case 2: 2x-1 = -9
- 2x = -8
- x = -4
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Solutions
Therefore, the solutions to the equation (2x-1)^2 = 81 are:
- x = 5
- x = -4
Verification
We can verify our solutions by plugging them back into the original equation:
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For x = 5:
- (2(5)-1)^2 = 9^2 = 81
- This solution is valid.
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For x = -4:
- (2(-4)-1)^2 = (-9)^2 = 81
- This solution is also valid.
Conclusion
We have successfully solved the equation (2x-1)^2 = 81 and found two solutions: x = 5 and x = -4. By taking the square root of both sides and considering both positive and negative values, we were able to isolate x and determine its possible values.