# How do you solve 3x^2 - 10 = 2x by completing the square?

May 10, 2016
1. Move the constant to the right
2. Make a = 1
3. Add on ${\left(\frac{b}{2}\right)}^{2}$ to both sides
4. Write as (x +- b/2)^2 =
5. Find square toot of both sides
6. Solve twice - pos and neg square root

$3 {x}^{2} - 10 = 2 x \Rightarrow 3 {x}^{2} - 2 x = 10$

${x}^{2} - \frac{2 x}{3} + \textcolor{red}{{\left(\frac{1}{3}\right)}^{2}} = \frac{10}{3} + \textcolor{red}{{\left(\frac{1}{3}\right)}^{2}}$
${\left(x - \frac{1}{3}\right)}^{2} = \frac{31}{9}$

$x - \frac{1}{3} = \pm \frac{\sqrt{31}}{3}$

$x = \frac{\sqrt{31}}{3} + \frac{1}{3} \text{ or } x = - \frac{\sqrt{31}}{3} + \frac{1}{3}$

$x = 2.189 \mathmr{and} x = - 1.523$