Question 802409
{{{x^2-x=8}}}

This is a quadratic equation. You can tell because 2 is the highest power. If you are solving for x, then you have to get all the terms on one side and an "=0" on the other. So you need to subtract 8 from both sides, resulting in {{{x^2-x-8=0}}}.  Now there at least two ways to solve this: Factoring, or the Quadratic Equation. This does not factor nicely, so we'll just use the Quadratic Equation {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}.

Quadratic Standard Form {{{Ax^2+Bx+C=0}}} is the form we need to use for this. Looking at the coefficients gives us our A=1, B=-1, and C=-8. We plug these into the equation to get our answer:

{{{x = (-(-1) +- sqrt( (-1)^2-4*(1)*(-8) ))/(2*(1)) }}}
{{{x = (1 +- sqrt(1+32))/2}}}
{{{x = (1 +- sqrt(33))/2}}}

And that is about as far as we can go without using a calculator to simplify. If you want a decimal answer, you can plug into the calculator {{{(1 + sqrt(33))/2}}} and  {{{(1 - sqrt(33))/2}}} to give you {{{x=3.372}}} and {{{x=-2.372}}}