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1

Solved example of Equations

$x^2+6x+8=0$
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 $c=8$

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

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

$x=\frac{-6\pm 2}{2}$
4

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

$x_1=\frac{-6+ 2}{2}\:\:,\:\:x_2=\frac{-6- 2}{2}$
5

Simplifying

$x_1=-2,\:x_2=-4$
6

We found that the two real solutions of the equation are

$x_1=-2,\:x_2=-4$