Question

BIG POINTS

Solve x2 + 9 x + 8 = 0 by completing the square. What are the solutions?
{1,-8}
{1, 8} (Not this one)
{-1,-8}

Answer 1

{-1, -8}

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.