%5E2%3D81.jpeg "(x-4)^2=81")
Solving the Equation (x-4)^2 = 81
This equation involves a squared term, which requires us to take the square root to isolate the variable 'x'. Let's break down the steps to solve it:
1. Taking the Square Root
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The first step is to take the square root of both sides of the equation. Remember that when taking the square root, we need to consider both positive and negative solutions:
√((x-4)^2) = ±√81
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Simplifying this gives us:
x - 4 = ±9
2. Isolating 'x'
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Now, we need to isolate 'x' by adding 4 to both sides of the equation:
x = 4 ± 9
3. Finding the Solutions
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This gives us two possible solutions:
x = 4 + 9 = 13
x = 4 - 9 = -5
Therefore, the solutions to the equation (x-4)^2 = 81 are x = 13 and x = -5.
Verification
To verify our solutions, we can substitute each value back into the original equation:
- For x = 13: (13 - 4)^2 = 9^2 = 81
- For x = -5: (-5 - 4)^2 = (-9)^2 = 81
Both solutions satisfy the original equation, confirming our results.