(x%2B2)-(x-5)(x%2B6)%3D-x.jpeg "(x-4)(x+2)-(x-5)(x+6)=-x")
Solving the Equation: (x-4)(x+2)-(x-5)(x+6)=-x
This article will guide you through solving the equation (x-4)(x+2)-(x-5)(x+6)=-x. We will use the distributive property and combine like terms to find the solution.
Expanding the Equation
First, we need to expand the equation by multiplying the terms in the parentheses:
- (x-4)(x+2): x² + 2x - 4x - 8 = x² - 2x - 8
- (x-5)(x+6): x² + 6x - 5x - 30 = x² + x - 30
Now, substitute the expanded terms back into the original equation:
(x² - 2x - 8) - (x² + x - 30) = -x
Simplifying the Equation
Next, simplify the equation by removing the parentheses and combining like terms:
x² - 2x - 8 - x² - x + 30 = -x
-3x + 22 = -x
Solving for x
Finally, solve for x by isolating the variable:
-3x + x = -22
-2x = -22
x = -22 / -2
x = 11
Conclusion
Therefore, the solution to the equation (x-4)(x+2)-(x-5)(x+6)=-x is x = 11. You can verify this solution by substituting it back into the original equation and confirming that both sides are equal.