Question

Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions?

Answer 1

So firstly, what two terms have a product of 8x^2 and a sum of 9x? That would be x and 8x. Replace 9x with x + 8x: $x^2+x+8x+8=0$

Next, factor x^2 + x and 8x + 8 separately. Make sure that they have the same quantity on the inside: $x(x+1)+8(x+1)=0$

Now you can rewrite the equation as $(x+8)(x+1)=0$

Now using zero product property, solve for x:

$x+8=0\\ x=-8\\ \\ x+1=0\\ x=-1$

In short, the solutions are {-1,-8}, or C.