# How do you solve using the completing the square method 2x^2-8x-3=0?

Jun 15, 2018

See below

#### Explanation:

First extracting common factor

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

Now complete square

$2 \left({\left(x - 2\right)}^{2} - 4 - \frac{3}{2}\right) = 0$ now re-arrange terms

$2 \left({\left(x - 2\right)}^{2} - \frac{11}{2}\right) = 0$

Now, using identity $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

$2 \left(\left(x - 2 + \sqrt{\frac{11}{2}}\right) \left(x - 2 - \sqrt{\frac{11}{2}}\right)\right) = 0$

Roots are $2 + \sqrt{\frac{11}{2}}$ and $2 - \sqrt{\frac{11}{2}}$