# How do you solve the equation x^2-3x-7=0 by completing the square?

Mar 3, 2018

color(blue)(x = 4.54, -1.54

#### Explanation:

${x}^{2} - 3 x - 7 = 0$

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

Adding ${\left(\frac{3}{2}\right)}^{2}$ to both sides,

x^2 - (2 * 3/2) * x) + (3/2)^2 = 7 + (3/2)^2 = 37/4

${\left(x - \left(\frac{3}{2}\right)\right)}^{2} = {\left(\sqrt{\frac{37}{4}}\right)}^{2}$

$x = \pm \sqrt{\frac{37}{4}} + \left(\frac{3}{2}\right)$

color(blue)(x= 4.54, -1.54