(x%2B7)%3D-18.jpeg "(x-2)(x+7)=-18")
Solving the Equation (x-2)(x+7) = -18
This article will guide you through the steps to solve the quadratic equation (x-2)(x+7) = -18.
1. Expand the Equation
First, we need to expand the left side of the equation by multiplying the two factors:
(x-2)(x+7) = x² + 5x - 14
Now our equation becomes:
x² + 5x - 14 = -18
2. Move All Terms to One Side
To solve this quadratic equation, we need to set it equal to zero. Add 18 to both sides:
x² + 5x + 4 = 0
3. Factor the Quadratic Expression
The quadratic expression on the left side can be factored as:
(x + 1)(x + 4) = 0
4. Solve for x
For the product of two factors to be zero, at least one of them must be zero. Therefore:
- x + 1 = 0 => x = -1
- x + 4 = 0 => x = -4
5. Solution
The solutions to the equation (x-2)(x+7) = -18 are x = -1 and x = -4.