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Solving the Equation (x-4)² = 16
This article will guide you through solving the equation (x-4)² = 16. We will explore the steps involved and understand the concepts behind the solution.
Understanding the Equation
The equation (x-4)² = 16 represents a quadratic equation. It involves a squared term, making it a bit more complex than a simple linear equation.
Solving for x
Here's how we can solve for x:
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Take the square root of both sides:
√[(x-4)²] = ±√16
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Simplify:
x - 4 = ±4
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Isolate x:
x = 4 ± 4
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Calculate the possible solutions:
- x = 4 + 4 = 8
- x = 4 - 4 = 0
Therefore, the solutions to the equation (x-4)² = 16 are x = 8 and x = 0.
Verification
We can verify our solutions by substituting them back into the original equation:
- For x = 8: (8-4)² = 4² = 16. This confirms the solution is correct.
- For x = 0: (0-4)² = (-4)² = 16. This also confirms the solution is correct.
Conclusion
We have successfully solved the quadratic equation (x-4)² = 16, finding the solutions x = 8 and x = 0. This demonstrates the process of solving a quadratic equation by taking the square root of both sides and then isolating the variable.