(Remember to set g(x) to zero).
For this, I will be completing the square. Firstly, what two terms have a product of 8x^2 and a sum of 6x? That would be 4x and 2x. Replace 6x with 2x + 4x: [tex] 0=-x^2+2x+4x-8 [/tex]
Next, factor -x^2 + 2x and 4x - 8 separately. Make sure that they have the same quantity on the inside of the parentheses: [tex] 0=-x(x-2)+4(x-2) [/tex]
Next, you can rewrite the equation as [tex] 0=(-x+4)(x-2) [/tex]
Now apply the Zero Product Property:
[tex] -x+4=0\\-x=-4\\x=4\\\\x-2=0\\x=2 [/tex]
The zeros of this equation are 4 and 2.
