(x-5)(x+2)=-6

2 min read Jun 17, 2024

Solving the Equation (x-5)(x+2) = -6

This article will guide you through the steps of solving the equation (x-5)(x+2) = -6. We will use algebraic manipulation to find the possible values of x that satisfy the equation.

Step 1: Expand the Left Side

First, we need to expand the left side of the equation by using the distributive property (or FOIL method).

(x - 5)(x + 2) = x² - 3x - 10

This gives us the new equation: x² - 3x - 10 = -6

Step 2: Move All Terms to One Side

To solve for x, we need to bring all terms to one side of the equation. Add 6 to both sides of the equation:

x² - 3x - 10 + 6 = 0

This simplifies to: x² - 3x - 4 = 0

Step 3: Factor the Quadratic Equation

Now we have a quadratic equation in standard form. We can factor this equation to find the solutions for x:

(x - 4)(x + 1) = 0

Step 4: Solve for x

To make the product of two factors equal to zero, at least one of the factors must be equal to zero. Therefore, we have two possible solutions:

x - 4 = 0 This gives us x = 4
x + 1 = 0 This gives us x = -1

Conclusion

The solutions to the equation (x-5)(x+2) = -6 are x = 4 and x = -1. You can verify these solutions by substituting them back into the original equation.