# Math Help - a^2+ab+c=0

1. ## a^2+ab+c=0

I think this is solvable, but I am stuck.

Given a^2+ab+c=0
solve for a.

3. ## Re: a^2+ab+c=0

hint:

$a^2 + ab + c = a^2 + ab + \frac{b^2}{4} + c - \frac{b^2}{4} = \left(a + \frac{b}{2}\right)^2 + c - \frac{b^2}{4}$

4. ## Re: a^2+ab+c=0

$a^2+ab=-c$

$4a^2+4ab=-4c$

$4a^2+4ab+b^2=b^2-4c$

$(2a+b)^2=b^2-4c$

$2a+b=\pm\sqrt{b^2-4c}$

$2a=-b\pm\sqrt{b^2-4c}$

$a=\frac{-b\pm\sqrt{b^2-4c}}{2}$

5. ## Re: a^2+ab+c=0

Thanks MarkFL2 and Deveno. The Quadratic equation is quite useful and has a whole page on wikipedia.