# How do you solve using the completing the square method x^2 – 5x + 10 = 0?

Apr 14, 2017

$x = \pm \frac{\sqrt{15}}{2} i + \frac{5}{2}$

#### Explanation:

To $\textcolor{b l u e}{\text{complete the square}}$

add (1/2" coefficient of the x-term")^2" to " x^2-5x

To retain the balance of the equation this should be added to both sides.

$\Rightarrow \text{ add } {\left(- \frac{5}{2}\right)}^{2} = \frac{25}{4}$

$\Rightarrow \left({x}^{2} - 5 x \textcolor{red}{+ \frac{25}{4}}\right) + 10 = 0 \textcolor{red}{+ \frac{25}{4}}$

$\Rightarrow {\left(x - \frac{5}{2}\right)}^{2} = \frac{25}{4} - 10$

$\Rightarrow {\left(x - \frac{5}{2}\right)}^{2} = - \frac{15}{4}$

Since the right side is negative, the solutions are complex.

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\sqrt{{\left(x - \frac{5}{2}\right)}^{2}} = \pm \sqrt{- \frac{15}{4}}$

$\Rightarrow x - \frac{5}{2} = \pm \frac{\sqrt{15}}{2} i$

$\Rightarrow x = \pm \frac{\sqrt{15}}{2} i + \frac{5}{2}$