# How do you solve x^2 + 1/2x = 1 by completing the square?

Jul 12, 2016

$x = 0.781 \text{ or } x = - 1.281$

#### Explanation:

The constant (1) is already on the RHS.

We need to add in a term so that the left hand side can be factored as (x +-?)^2

The missing term is found by dividing the coefficient of x by 2 and then squaring the answer. The result must be added to BOTH sides.

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

${\left(x + \frac{1}{4}\right)}^{2} = 1 \frac{1}{16} = \frac{17}{16}$

$x + \frac{1}{4} = \pm \sqrt{\frac{17}{16}}$

$x = \pm \frac{\sqrt{17}}{4} - \frac{1}{4} = \frac{\pm \sqrt{17} - 1}{4}$

$x = 0.781 \text{ or } x = - 1.281$