Solving the Equation: (x-6)(x+6)-(x+3)^2=9
This article will guide you through the steps to solve the equation (x-6)(x+6)-(x+3)^2=9.
Expanding and Simplifying
Let's start by expanding the equation:
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Expand the product: (x-6)(x+6) = x^2 - 36 (using the difference of squares pattern)
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Expand the square: (x+3)^2 = x^2 + 6x + 9
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Substitute: Our equation now becomes: x^2 - 36 - (x^2 + 6x + 9) = 9
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Simplify: x^2 - 36 - x^2 - 6x - 9 = 9
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Combine like terms: -6x - 45 = 9
Solving for x
- Isolate the x term: -6x = 54
- Solve for x: x = -9
Conclusion
Therefore, the solution to the equation (x-6)(x+6)-(x+3)^2=9 is x = -9.