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

Quadratic Formula Complete the Square Factor


Quadratic Formula

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

\[ x = \frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a} \]
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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. \[x=\frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a} \]
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Factor

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. \[jx+k=0\]\[mx+n=0\]
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