Answer:
{-1, -8}
Step-by-step explanation:
We can get the constant "out of the way" by subtracting it:
x² +9x = -8
Now we can add the square of half the x-coefficient:
x² +9x +4.5² = -8 +4.5² . . . . . . . . complete the square
(x +4.5)² = 12.25 . . . . . . . . . . . . . . simplify
x + 4.5 = ±√12.25 = ±3.5 . . . . . . . take the square root
x = -4.5 ± 3.5 . . . . . . . . . . . . . . . . . subtract 4.5
x ∈ {-1, -8} . . . . . . this is a list of the solutions
_____
If you factor the equation, you get
(x +1)(x +8) = 0
The solutions are the values of x that make the factors be zero, hence the opposite of the constants in the binomial factors: -1, -8.
