# How do you solve 3/2=11/(2m)-m-2/m?

Jan 24, 2016

$x = - 2.766 \text{ or " + 1.266" }$ to 3 decimal places

If you need more detail about the calc go to my profile page and put a not on it!

#### Explanation:

$\frac{3}{2} = \frac{11 - 2 {m}^{2} - 4}{2 m}$

$6 m = 22 - 4 {m}^{2} - 8$

$4 {m}^{2} + 6 m - 14 = 0$

(am+?)(bm+?)
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$\textcolor{b l u e}{\text{Attempt 1}}$
$\left(4 m - 2\right) \left(m + 7\right) \to 4 {m}^{2} + 28 m - 2 m - 14 \textcolor{red}{\text{ Fail!}}$

$\textcolor{b l u e}{\text{Attempt 2}}$
$\left(m - 2\right) \left(4 m + 7\right) \to 4 {m}^{2} + 7 m - 2 m - 14 \textcolor{red}{\text{ Fail!}}$

$\textcolor{b l u e}{\text{Attempt 3}}$
$\left(2 m - 2\right) \left(2 m + 7\right) \to 4 {m}^{2} + 14 m - 4 m - 14 \textcolor{red}{\text{ Fail!}}$

$\textcolor{b l u e}{\text{Attempt 4}}$

$x = \frac{- 6 \pm \sqrt{{6}^{2} - 4 \left(4\right) \left(- 14\right)}}{2 \left(4\right)}$

$x = \frac{- 6 \pm \sqrt{36 + 224}}{8}$

$x = \frac{- 6 \pm \sqrt{260}}{8}$

$x = \frac{- 6 \pm 2 \sqrt{65}}{8}$

(-6-

$x = - 2.766 \text{ or " + 1.266" }$ to 3 decimal places