# How do you solve by completing the square: x^2 + 4x + 2 = 0?

Mar 30, 2015

x^2+4x+2=0#

Remove the $2$ from the left side expression by subtracting $2$ from both sides:
${x}^{2} + 4 x = - 2$

If the left side is to be a square its non-$x$ term must be the coefficient of $x$ divided by $2$ then squared (i..e.${\left(\frac{4}{2}\right)}^{2} = 4$);
add this amount to both sides:
${x}^{2} + 4 x + 4 = + 2$

Rewrite the left-hand side as a square:
${\left(x + 2\right)}^{2} = 2$

Take the square root of both sides
$x + 2 = \pm \sqrt{2}$

Isolate $x$ on the rights side (by subtracting $2$ from both sides)
$x = - 2 \pm \sqrt{2}$

So the solutions are
$x = - 2 + \sqrt{2}$ and $x = - 2 - \sqrt{2}$