(x%2B5)-30%3D0-in-factored-form.jpeg "(x+4)(x+5)-30=0 In Factored Form")
Solving (x+4)(x+5)-30=0 in Factored Form
This problem involves solving a quadratic equation in factored form. Let's break down the steps:
1. Expand the Expression:
First, we need to expand the left side of the equation by multiplying the binomials:
(x+4)(x+5) - 30 = 0
x² + 9x + 20 - 30 = 0
2. Simplify the Expression:
Combine the constant terms:
x² + 9x - 10 = 0
3. Factor the Quadratic Expression:
Now, we need to find two numbers that multiply to -10 and add up to 9. These numbers are 10 and -1:
x² + 10x - x - 10 = 0
x(x + 10) - 1(x + 10) = 0
Now we can factor out (x + 10):
(x + 10)(x - 1) = 0
4. Solve for x:
For the product of two terms to be zero, at least one of them must be zero. Therefore:
- x + 10 = 0 => x = -10
- x - 1 = 0 => x = 1
Solution:
Therefore, the solutions to the equation (x+4)(x+5)-30=0 in factored form are x = -10 and x = 1.