# How do you solve using the completing the square method x^2 + 8x – 2 = 0?

Aug 24, 2016

$x = - 4 - 3 \sqrt{2}$ or $x = - 4 + 3 \sqrt{2}$

#### Explanation:

Compare ${x}^{2} + 8 x - 2 = 0$ with the identity ${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$. Note that to complete the square we have to add square of half of the coefficient of $x$. As coefficient of x is 8 we should add and subtract ${4}^{2}$. Hence,

${x}^{2} + 8 x - 2 = 0$ can be written as

${x}^{2} + 8 x + 16 - 16 - 2 = 0$ or

${\left(x + 4\right)}^{2} - 18 = 0$ or

${\left(x + 4\right)}^{2} - {\left(\sqrt{18}\right)}^{2} = 0$ or

${\left(x + 4\right)}^{2} - {\left(3 \sqrt{2}\right)}^{2} = 0$ or

$\left(x + 4 + 3 \sqrt{2}\right) \left(x + 4 - 3 \sqrt{2}\right) = 0$ or

$x = - 4 - 3 \sqrt{2}$ or $x = - 4 + 3 \sqrt{2}$