# How do you complete the square to solve x^2 + 6x + 34 = 0?

Jun 7, 2015

${x}^{2} + 6 x + 34 = 0$
can be written as
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 6 x = - 34$

completing the square:
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 6 x + 9 = - 25$
$\textcolor{w h i t e}{\text{XXXX}}$${\left(x + 3\right)}^{2} = - 25$
take the square root of both sides
$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 = \sqrt{- 25}$$\textcolor{w h i t e}{\text{XXXX}}$(Note: no Real solutions)

$\textcolor{w h i t e}{\text{XXXX}}$$x = - 3 \pm 5 i$