Home Enter integer, fraction, or decimal values for A, B, and C and select a method to solve.

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

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

Complete the Square

Move c to the right side of the equation. $ax^2+bx = -c$
Factor a out of both terms on the left side. $a(x^2+\frac{b}{a}x) = -c$
Divide both sides by a. $x^2+\frac{b}{a}x = \frac{-c}{a}$
Divide the coefficient of the x term by 2. Square that and add to both sides. $x^2+\frac{b}{a}x + (\frac{b}{2a})^2 = \frac{-c}{a} + (\frac{b}{2a})^2$
Factor the left side. Combine the terms on the right side. $(x+\frac{b}{2a})^2 = \frac{b^2-4ac}{4a^2}$
Square root both sides. $x+\frac{b}{2a} = \pm \frac{\sqrt{b^2-4ac}}{2a}$
Solve for x. $x=\frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}$
Rewrite the middle term using two factors whose product equals a*c and sum equals b. Group the terms in pairs. $(ax^2+sx)(+tx+c) = 0$
Factor each pair. $mx(jx+k)+n(jx+k)$
Factor the shared binomial. $(jx+k)(mx+n) = 0$
Set each binomial equal to 0. Solve for x. $jx+k=0$$mx+n=0$