# How do you solve using the completing the square method  0=x^2-3x-6?

Aug 14, 2017

$x = \frac{3}{2} \pm {\left(33\right)}^{\frac{1}{2}} / 2$

#### Explanation:

We need to add a number to create the constant
${\left(\frac{b}{2}\right)}^{2}$ which will make the perfect square ${\left(x - \left(\frac{b}{2}\right)\right)}^{2}$
Since b = - 3 then ${\left(\frac{b}{2}\right)}^{2} = \frac{9}{4}$
But we already have - 6 = - 24/4 so we need to add 33/4
And we also need to subtract 33/4 to keep the equation true
This results in
${\left(x - \left(\frac{3}{2}\right)\right)}^{2} = \frac{33}{4}$
Taking the root and adding 3/2 to both sides
gives the result
$x = \frac{3}{2} \pm {\left(33\right)}^{\frac{1}{2}} / 2$