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Solving the Equation (x-7)^2 = 9
This article will guide you through the process of solving the equation (x-7)² = 9. This equation involves a squared term, and we will use the square root property to find the solution.
Understanding the Equation
The equation (x-7)² = 9 represents a quadratic equation in the form of a perfect square trinomial. It describes a situation where the square of the quantity (x-7) is equal to 9.
Solving using the Square Root Property
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Take the square root of both sides: To get rid of the square, we take the square root of both sides of the equation. Remember that the square root of a number can be both positive and negative.
√(x-7)² = ±√9
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Simplify: The square root of (x-7)² is simply (x-7), and the square root of 9 is 3.
x - 7 = ±3
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Isolate x: Add 7 to both sides of the equation.
x = 7 ± 3
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Calculate the two possible solutions: We get two possible solutions:
- x = 7 + 3 = 10
- x = 7 - 3 = 4
Verification
We can verify our solutions by substituting each value of x back into the original equation:
- For x = 10: (10 - 7)² = 3² = 9. This solution is valid.
- For x = 4: (4 - 7)² = (-3)² = 9. This solution is also valid.
Conclusion
Therefore, the solutions to the equation (x-7)² = 9 are x = 10 and x = 4.