(x-2)%3D60.jpeg "(x+5)(x-2)=60")
Solving the Equation (x+5)(x-2)=60
This article will guide you through the process of solving the quadratic equation (x+5)(x-2)=60. We will use a combination of algebraic manipulation and the quadratic formula to find the solutions.
Expanding the Equation
First, we need to expand the left side of the equation by multiplying the binomials:
(x+5)(x-2) = x² + 3x - 10
Now our equation becomes:
x² + 3x - 10 = 60
Rearranging into Standard Form
Next, we need to rearrange the equation into standard quadratic form, which is ax² + bx + c = 0:
x² + 3x - 70 = 0
Solving using the Quadratic Formula
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
Where:
- a = 1
- b = 3
- c = -70
Substituting these values into the formula, we get:
x = (-3 ± √(3² - 4 * 1 * -70)) / (2 * 1)
x = (-3 ± √(289)) / 2
x = (-3 ± 17) / 2
Finding the Solutions
This gives us two possible solutions:
- x₁ = (-3 + 17) / 2 = 7
- x₂ = (-3 - 17) / 2 = -10
Conclusion
Therefore, the solutions to the equation (x+5)(x-2)=60 are x = 7 and x = -10.