# How do you solve using the completing the square method x^2 − x = 30?

Aug 6, 2016

$x = - 5 , 6$

#### Explanation:

${x}^{2} - x = 30$

1) Check the constant term is on the right side if not bring it to the right side .
2) Check the coefficient of x^2 is 1 if not Make the coefficient of x^2 as 1

${x}^{2} - x = 30$

Add both side ${\left(c o e f f i c i e n t o f \frac{x}{2}\right)}^{2}$

Coefficient of x is -1 so add ${\left(- \frac{1}{2}\right)}^{2}$, both side

${x}^{2} - x + {\left(\frac{1}{2}\right)}^{2} = 30 + {\left(\frac{1}{2}\right)}^{2}$ use the identity ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

${x}^{2} - x + {\left(\frac{1}{2}\right)}^{2} = {\left(x - \frac{1}{2}\right)}^{2}$

${\left(x - \frac{1}{2}\right)}^{2} = 30 + \frac{1}{4}$

${\left(x - \frac{1}{2}\right)}^{2} = \frac{121}{4}$
squaring on both side

$\left(x - \frac{1}{2}\right) = \pm \sqrt{\frac{121}{4}}$

$\left(x - \frac{1}{2}\right) = \pm \frac{11}{2}$

$x = \frac{1}{2} + \frac{11}{2} , x = \frac{1}{2} - \frac{11}{2}$
$x = \frac{12}{2} \mathmr{and} x = - \frac{10}{2}$

$x = - 5 , 6$