Answer:
x = -19 or x = -1
Step-by-step explanation:
[tex] x^2 + 20x + 11 = -8 [/tex]
We need the quadratic equation in the form
[tex] ax^2 + bx + c = 0 [/tex],
so we add 8 to both sides.
[tex] x^2 + 20x + 19 = 0 [/tex]
Now we have an equation of the form x^2 + ax + b = 0.
We need to factor the quadratic equation. To factor it, we need two numbers, p and q, whose product is b and whose sum is a. Then the factoring is (x + p)(x + q).
In our case, b = 19 and a = 20. We need two numbers that multiply to 19 and add to 20. The numbers are 19 and 1. Our p and q are 19 and 1.
(x + 19)(x + 1) = 0
Since a product of two factors equals zero, either one factor equals zero, or the other factor equals zero. We set each factor equal to zero and solve both equations for x.
x + 19 = 0 or x + 1 = 0
x = -19 or x = -1
