# Question 85932

Mar 8, 2017

$x = - 1$ and $x = - \frac{4}{5}$

#### Explanation:

$5 {x}^{2} + 9 x = - 4$

$\therefore 5 x + 9 x + 4 = 0$

$\therefore \left(x + 1\right) \left(5 x + 4\right)$

$\therefore x + 1 = 0$ and $5 x + 4 = 0$

:.color(blue)(x=-1 and $5 x = - 4$

:.color(blue)(x=-1 and color(blue)(x=-4/5

substitute color(blue)(x=-1

$\therefore 5 {\left(\textcolor{b l u e}{- 1}\right)}^{2} + 9 \left(\textcolor{b l u e}{- 1}\right) = - 4$

$\therefore 5 \left(\textcolor{b l u e}{- 1}\right) \left(\textcolor{b l u e}{- 1}\right) - 9 = - 4$

$\therefore 5 - 9 = - 4$

:.color(blue)(-4=-4

substitute color(blue)(x=-4/5

$\therefore 5 {\textcolor{b l u e}{\left(- \frac{4}{5}\right)}}^{2} + 9 \left(\textcolor{b l u e}{- \frac{4}{5}}\right) = - 4$

$\therefore 5 \left(\textcolor{b l u e}{- \frac{4}{5}}\right) \left(\textcolor{b l u e}{- \frac{4}{5}}\right) + 9 \left(\textcolor{b l u e}{- \frac{4}{5}}\right) = - 4$

$\therefore 5 \left(\frac{16}{25}\right) - \left(\frac{36}{5}\right) = - 4$

$\therefore \frac{80}{25} - \frac{36}{5} = - \frac{4}{1}$

$\therefore \frac{80 - 180 = - 100}{25}$

:.color(blue)(-100=-100#