How do you solve x^2+8x-10=0 by completing the square?

Mar 19, 2018

$x = - 4 \pm \sqrt{26}$

Explanation:

$\text{using the method of "color(blue)"completing the square}$

• " the coefficient of the "x^2" term must be 1 which it is"

• " add/subtract "(1/2" coefficient of the x-term")^2" to"
${x}^{2} + 8 x$

${x}^{2} + 2 \left(4\right) x \textcolor{red}{+ 16} \textcolor{red}{- 16} - 10 = 0$

$\Rightarrow {\left(x + 4\right)}^{2} - 26 = 0$

$\Rightarrow {\left(x + 4\right)}^{2} = 26$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\Rightarrow x + 4 = \pm \sqrt{26} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\text{subtract 4 from both sides}$

$\Rightarrow x = - 4 \pm \sqrt{26} \leftarrow \textcolor{red}{\text{exact solutions}}$