# How do you complete the square to solve  2x^2 + 6x =5?

May 24, 2015

$2 {x}^{2} + 6 x = 5$

Extract the common constant factor on the left side
$2 \left({x}^{2} + 3 x\right) = 5$

Complete the square
$2 \left({x}^{2} + 3 x + {\left(\frac{3}{2}\right)}^{2}\right) = 5 + \frac{9}{2}$

Re-write as a square equal to a constant
${\left(x + \frac{3}{2}\right)}^{2} = \frac{19}{4}$

Take the square root of both sides
$x + \frac{3}{2} = \pm \frac{\sqrt{19}}{2}$

Isolate $x$ for the final solution
$x = \frac{- 3 \pm \sqrt{19}}{2}$