# How do you solve using the completing the square method x^2 = 2x + 4?

Oct 26, 2017

$x = 3.236 \text{ "or" } x = - 1.236$

#### Explanation:

In the equation ${x}^{2} - 2 x - 4 = 0$, $\text{ } - 4$ is not ${\left(\frac{b}{2}\right)}^{2}$

${x}^{2} - 2 x \text{ "=4" } \leftarrow$move $- 4$ to the right side

Add $\textcolor{b l u e}{{\left(\frac{b}{2}\right)}^{2}}$ to both sides $\textcolor{b l u e}{{\left(\frac{- 2}{2}\right)}^{2} = 1}$

${x}^{2} - 2 x \textcolor{b l u e}{+ 1} = 4 \textcolor{b l u e}{+ 1}$

$\text{ } {\left(x - 1\right)}^{2} = 5$

$\text{ } x - 1 = \pm \sqrt{5}$

$\text{ } x = + \sqrt{5} + 1 \textcolor{w h i t e}{\times \times \times} \mathmr{and} x = - \sqrt{5} + 1$

$\text{ } x = + \sqrt{5} + 1 \textcolor{w h i t e}{\times \times \times} \mathmr{and} x = - \sqrt{5} + 1$

$x = 3.236 \text{ "or" } x = - 1.236$