# How do you solve using the completing the square method 0=3x^2-11x+6?

Apr 22, 2016

$x = 3$
$x = \frac{2}{3}$

#### Explanation:

Given -

$3 {x}^{2} - 11 x + 6 = 0$
Divide each term by the coefficient of ${x}^{2}$
${x}^{2} - \frac{11}{3} x + 2 = 0$
Take the constant term to the right
${x}^{2} - \frac{11}{3} x = - 2$
Divide the coefficient of $x$by $2$ and add the
thus received value to both sides after squaring it.
${x}^{2} - \left(\frac{11}{3} \times \frac{1}{2}\right) x + {\left(\frac{11}{6}\right)}^{2} = - 2 + {\left(\frac{11}{6}\right)}^{2}$
${x}^{2} - \frac{11}{6} x + \frac{121}{36} = - 2 + \frac{121}{36}$
${x}^{2} - \frac{11}{6} + \frac{121}{36} = \frac{\left(- 72\right) + 121}{36} = \frac{49}{36}$
Take square root on both sides
$\left(x - \frac{11}{6}\right) = \pm \sqrt{\frac{49}{36}} = \pm \frac{7}{6}$
$x = \frac{7}{6} + \frac{11}{6} = \frac{7 + 11}{6} = \frac{18}{6} = 3$
$x = - \frac{7}{6} + \frac{11}{6} = \frac{- 7 + 11}{6} = \frac{4}{6} = \frac{2}{3}$