# How do you solve x^2-10x+8=0 using the quadratic formula?

Feb 29, 2016

$x = 5 \pm \sqrt{17}$

#### Explanation:

$1$. Determine the $a$, $b$, and $c$ values of the equation. Recall that the general quadratic equation written in standard form is: $a {x}^{2} + b x + c = 0$.

${x}^{2} - 10 x + 8 = 0$

$\textcolor{red}{1} {x}^{2}$ $\textcolor{\mathmr{and} a n \ge}{- 10} x$ $\textcolor{b l u e}{+ 8} = 0$

$a = \textcolor{red}{1} \textcolor{w h i t e}{X X X} b = \textcolor{\mathmr{and} a n \ge}{- 10} \textcolor{w h i t e}{X X X} c = \textcolor{b l u e}{8}$

$2$. Substitute the $a$, $b$, and $c$ values into the quadratic formula.

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

$x = \frac{- \left(\textcolor{\mathmr{and} a n \ge}{- 10}\right) \pm \sqrt{{\left(\textcolor{\mathmr{and} a n \ge}{- 10}\right)}^{2} - 4 \left(\textcolor{red}{1}\right) \left(\textcolor{b l u e}{8}\right)}}{2 \left(\textcolor{red}{1}\right)}$

$3$. Solve for $x$.

$x = \frac{10 \pm \sqrt{100 - 32}}{2}$

$x = \frac{10 \pm \sqrt{68}}{2}$

$x = \frac{10 \pm 2 \sqrt{17}}{2}$

$x = \frac{2 \left(5 \pm \sqrt{17}\right)}{2 \left(1\right)}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(5 \pm \sqrt{17}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(1\right)}$

$\textcolor{g r e e n}{x = 5 \pm \sqrt{17}}$

$\therefore$, $x = 5 \pm \sqrt{17}$.