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: [tex] x^2+x+8x+8=0 [/tex]
Next, factor x^2 + x and 8x + 8 separately. Make sure that they have the same quantity on the inside: [tex] x(x+1)+8(x+1)=0 [/tex]
Now you can rewrite the equation as [tex] (x+8)(x+1)=0 [/tex]
Now using zero product property, solve for x:
[tex] x+8=0\\ x=-8\\ \\ x+1=0\\ x=-1 [/tex]
In short, the solutions are {-1,-8}, or C.
