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(x-3)(x+4)+8=x

2 min read Jun 17, 2024
(x-3)(x+4)+8=x

Solving the Equation (x-3)(x+4)+8=x

This article will guide you through the process of solving the equation (x-3)(x+4)+8=x. We will use algebraic manipulations to isolate the variable x and find its value.

Expanding and Simplifying

  1. Expand the product: Begin by expanding the left side of the equation using the distributive property (FOIL method): (x-3)(x+4) = x² + 4x - 3x - 12 = x² + x - 12

  2. Rewrite the equation: Now our equation becomes: x² + x - 12 + 8 = x

  3. Combine like terms: Simplify the equation by combining the constant terms: x² + x - 4 = x

Solving the Quadratic Equation

  1. Move all terms to one side: Subtract x from both sides to get all terms on the left side: x² - 4 = 0

  2. Factor the equation: The left side of the equation can be factored as a difference of squares: (x + 2)(x - 2) = 0

  3. Solve for x: For the product of two factors to be zero, at least one of the factors must be zero. Therefore: x + 2 = 0 or x - 2 = 0

    Solving these equations gives us: x = -2 or x = 2

Conclusion

The solutions to the equation (x-3)(x+4)+8=x are x = -2 and x = 2. You can verify these solutions by substituting them back into the original equation and checking if they satisfy it.

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