I have the equation $\displaystyle x^2-x=-147$.
I played around with it but couldn't find away to get a definite answer without having to use trial and error.
Thanks!
there is good reason you had problems. this has no real solutions
if you bring everything to one side: $\displaystyle x^2 - x + 147 = 0$
and apply the quadratic formula: $\displaystyle x = \frac {1 \pm \sqrt{1 - 4(147)}}2$
obviously what is under the square root is negative, thus we have complex solutions.
Technically yes.
$\displaystyle x^2 - x + 147 = \left ( x - \frac{1}{2} - i~\frac{\sqrt{587}}{2} \right ) \left ( x - \frac{1}{2} + i~\frac{\sqrt{587}}{2} \right )$
As Jhevon pointed out, there are no real solutions to this problem. And the factorization is awful looking. Stick with the quadratic formula for this one; not every quadratic factors nicely.
-Dan
I used the quadratic formula. it is derived by completing the square. basically it says, for any quadratic of the form $\displaystyle y = ax^2 + bx + c$, the roots of the quadratic (that is, the solutions to $\displaystyle ax^2 + bx + c = 0$) are given by:
$\displaystyle x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$
It's derivation is quite nice:
Quadratic Formula Derivation
But you will need to know how to complete the square. It is a necessary prerequisite.
This is hard stuff, so take your time with it and don't get yourself down if you can't understand it after a while.