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}

  {-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.