# How do you solve x^2-3x=28 by completing the square?

Mar 3, 2018

#### Answer:

color(green)(x = 7, -4

#### Explanation:

${x}^{2} - 3 x = 28$

Add ${\left(\frac{3}{2}\right)}^{2}$ to both sides.

${x}^{2} - \left(2 \cdot \left(\frac{3}{2}\right) \cdot x\right) + {\left(\frac{3}{2}\right)}^{2} = 28 + {\left(\frac{3}{2}\right)}^{2}$

${\left(x - \frac{3}{2}\right)}^{2} = \frac{121}{4} = {\left(\frac{11}{2}\right)}^{2}$

$x - \frac{3}{2} = \pm \frac{11}{2}$

$x = \pm \frac{11}{2} + \frac{3}{2}$

color(green)(x = 7, -4