Answer:
The roots are {-4, 2}.
Step-by-step explanation:
It seems strange to have x terms on both sides of your equation. If this is indeed the correct equation, then
x^2-x-8=-3x becomes x^2 +3x - x - 8= 0, and this latter result simplifies to
x^2 + 2x - 8 = 0.
One set of factors of -8 is {-2, 4} and another is {1, -8). Hence we could try evaluating this quadratic at x = 4:
4^2 + 2(4) - 8 = 16 (since this is not zero, 4 is not a root and (x - 4) is not a factor.
Try x = -4 instead:
(-4)^2 + 2(-4) - 8 = 0 simplifies to 16 - 8 - 8 = 0, which is true.
Then x + 4 is a factor and x - 2 is another. Multiplying these two together as a check results in the given x^2- x - 8 = -3x.
The roots are {-4, 2}.
