# How do you solve by completing the square 2x^2-6x-20=0?

Mar 23, 2018

${x}_{1} = - 2$ and ${x}_{2} = 5$

#### Explanation:

$2 {x}^{2} - 6 x - 20 = 0$

$2 \cdot \left({x}^{2} - 3 x - 10\right) = 0$

$2 \cdot \left({x}^{2} - 3 x + \frac{9}{4} - \frac{49}{4}\right) = 0$

$2 \cdot \left({\left(x - \frac{3}{2}\right)}^{2} - {\left(\frac{7}{2}\right)}^{2}\right) = 0$

$2 \left(x - \frac{3}{2} + \frac{7}{2}\right) \left(x - \frac{3}{2} - \frac{7}{2}\right) = 0$

$2 \left(x + 2\right) \left(x - 5\right) = 0$

Thus, ${x}_{1} = - 2$ and ${x}_{2} = 5$