Question 23507
This is a quadratic equation {{{x^2 = x+6}}} so you might be thinking of the quadratic formula that looks like this:{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} .  However, this problem just might factor, and this is MUCH easier than the quadratic formula when the problem factors!


{{{x^2 = x+6}}} 


The first step is to set the equation equal to zero.  You can either take everything to the right side or the left side, but I recommend that you arrange the terms so the {{{x^2}}} term is positive.  In this case, it means to take everything to the left side.  Subtract x and 6 from both sides:

{{{x^2 = x+6}}} 
{{{x^2-x -6 = x+6-x -6}}}
{{{x^2 - x -6=0}}}


This just happens to factor!
{{{(x-3)(x+2) =0}}}


There are TWO solutions:
x-3 = 0, so x= 3
x+2 = 0, so x=-2


Final answer:  x= 3 or x= -2


R^2 at SCC