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Quadratic formula Calculator

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1

Example

$x^2+6x-7=0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=6$ and $c=-7$

$x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
3

Substituting the values of the coefficients of the equation in the quadratic formula

$x=\frac{6\left(-1\right)\pm \sqrt{28+6^2}}{2}$
4

Multiply $-1$ times $6$

$x=\frac{-6\pm \sqrt{28+6^2}}{2}$
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Calculate the power

$x=\frac{-6\pm \sqrt{28+36}}{2}$
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Add the values $36$ and $28$

$x=\frac{-6\pm \sqrt{64}}{2}$
7

Calculate the power

$x=\frac{-6\pm 8}{2}$
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To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x_1=\frac{-6+ 8}{2}\:\:,\:\:x_2=\frac{-6- 8}{2}$
9

Simplifying

$x_1=1,\:x_2=-7$
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We found that the two real solutions of the equation are

$x_1=1,\:x_2=-7$

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