(x+2)(x-2)-(x+1)^2=7

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+2)(x-2)-(x+1)^2=7

This article will guide you through the process of solving the equation (x+2)(x-2)-(x+1)^2=7. We will use algebraic manipulation to isolate the variable x and find its solution(s).

Simplifying the Equation

1. Expand the products:

   • (x+2)(x-2) is a difference of squares: (x+2)(x-2) = x² - 4
   • (x+1)² is a perfect square: (x+1)² = x² + 2x + 1

2. Substitute the expanded expressions back into the original equation: x² - 4 - (x² + 2x + 1) = 7

3. Simplify by distributing the negative sign: x² - 4 - x² - 2x - 1 = 7

4. Combine like terms: -2x - 5 = 7

Solving for x

1. Isolate the x term: -2x = 12

2. Divide both sides by -2: x = -6

Conclusion

Therefore, the solution to the equation (x+2)(x-2)-(x+1)^2=7 is x = -6.