# How do you solve using the completing the square method m^2 - 10m = 3?

Apr 26, 2017

$m = 10.29 \text{ or } m = 0.29$

#### Explanation:

You would like to change the given equation into the form

${\left(x + b\right)}^{2} = c$ so that you can find the square roots and solve.

${m}^{2} \textcolor{b l u e}{- 10} m = 3$

Add on $\textcolor{b l u e}{{\left(\frac{b}{2}\right)}^{2}}$ to both sides: $\textcolor{b l u e}{{\left(\frac{- 10}{2}\right)}^{2} = 25}$

${m}^{2} - 10 m \textcolor{b l u e}{+ 25} = 3 \textcolor{b l u e}{+ 25}$

$\textcolor{w h i t e}{\ldots .} {\left(m - 5\right)}^{2} \text{ } = 28$

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} m - 5 = \pm \sqrt{28}$

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots . .} m = 5 \pm \sqrt{28}$

$m = 10.29 \text{ or } m = 0.29$