a^2+ab+c=0

**wolfv** · January 5th 2013, 11:05 PM

I think this is solvable, but I am stuck.

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

Thanks for your help.

**MarkFL** · January 5th 2013, 11:13 PM

Hint: Use the quadratic formula.

**Deveno** · January 5th 2013, 11:55 PM

hint:

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

**MarkFL** · January 6th 2013, 12:44 AM

$a^2+ab=-c$

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

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

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

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

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

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

**wolfv** · January 6th 2013, 05:29 AM

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

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