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Quadratic formula Calculator

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1

Solved example of quadratic formula

$t^2+8t-9=0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=8$ and $c=-9$. Then substitute the values of the coefficients of the equation in the quadratic formula:

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

$t=\frac{-8\pm \sqrt{8^2-4-9}}{2}$
3

Calculate the power $8^2$

$t=\frac{-8\pm \sqrt{64-4-9}}{2}$
4

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$t=\frac{-8+\sqrt{64-4-9}}{2},\:t=\frac{-8-1\sqrt{64-4-9}}{2}$
5

Split the fraction $\frac{-8-1\sqrt{64-4-9}}{2}$ in two terms with common denominator $2$

$t=\frac{-8}{2}+\frac{\sqrt{64-4-9}}{2},\:t=\frac{-8}{2}+\frac{-1\sqrt{64-4-9}}{2}$
6

Solve the equation ($1$)

$t=\frac{-8}{2}+\frac{\sqrt{64-4-9}}{2}$
7

Solve the equation ($2$)

$t=\frac{-8}{2}+\frac{-1\sqrt{64-4-9}}{2}$
8

The $2$ solutions of the equation are

$t=-4+\frac{\sqrt{64-4-9}}{2},\:t=-4-0.5\sqrt{64-4-9}$

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