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(x-6)(x+6)-(x+3)^2=9

less than a minute read Jun 17, 2024
(x-6)(x+6)-(x+3)^2=9

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:

  1. Expand the product: (x-6)(x+6) = x^2 - 36 (using the difference of squares pattern)

  2. Expand the square: (x+3)^2 = x^2 + 6x + 9

  3. Substitute: Our equation now becomes: x^2 - 36 - (x^2 + 6x + 9) = 9

  4. Simplify: x^2 - 36 - x^2 - 6x - 9 = 9

  5. Combine like terms: -6x - 45 = 9

Solving for x

  1. Isolate the x term: -6x = 54
  2. Solve for x: x = -9

Conclusion

Therefore, the solution to the equation (x-6)(x+6)-(x+3)^2=9 is x = -9.

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