(x-2)%3D60.jpeg "(x+9)(x-2)=60")
Solving the Quadratic Equation: (x+9)(x-2) = 60
This article will guide you through the steps of solving the quadratic equation (x+9)(x-2) = 60. Let's break it down:
1. Expanding the Equation
First, we need to expand the left side of the equation by multiplying the binomials:
(x+9)(x-2) = x² + 7x - 18
Now, our equation looks like this:
x² + 7x - 18 = 60
2. Simplifying the Equation
Next, we need to move all the terms to one side of the equation to set it equal to zero:
x² + 7x - 78 = 0
3. Factoring the Quadratic Expression
Now, we need to factor the quadratic expression on the left side of the equation:
(x+13)(x-6) = 0
4. Solving for x
Finally, we can solve for x by setting each factor equal to zero:
x+13 = 0 or x-6 = 0
Solving for x in each equation, we get:
x = -13 or x = 6
5. Solution
Therefore, the solutions to the quadratic equation (x+9)(x-2) = 60 are x = -13 and x = 6.