# How do you solve 4x^2+5=10x by completing the square?

Jun 4, 2017

$x = 1.809 \mathmr{and} x = 0.691$

#### Explanation:

Re-arrange the equation to be equal to $0$.

$4 {x}^{2} - 10 x + 5 = 0 \text{ } \leftarrow$ make $1 {x}^{2} \rightarrow \div 4$

${x}^{2} - \frac{5}{2} x \textcolor{red}{+ \frac{5}{4}} = 0$

${x}^{2} - \frac{5}{2} x \textcolor{w h i t e}{\ldots \ldots . .} = \textcolor{red}{- \frac{5}{4}}$

${x}^{2} - \frac{5}{2} x \textcolor{b l u e}{+ \frac{25}{16}} = - \frac{5}{4} \textcolor{b l u e}{+ \frac{25}{16}} \text{ } \leftarrow$Add$\textcolor{b l u e}{{\left(\frac{b}{2}\right)}^{2}}$ to both sides#

${\left(x - \frac{5}{4}\right)}^{2} \textcolor{w h i t e}{\ldots .} = \frac{5}{16}$

$x - \frac{5}{4} = \pm \sqrt{\frac{5}{16}}$

$x = + \sqrt{\frac{5}{16}} + \frac{5}{4} = 1.809$

$x = - \sqrt{\frac{5}{16}} + \frac{5}{4} = 0.691$