# How do you solve 7x ^ { 2} - 10x = - 3?

Mar 3, 2017

$x = 1$

#### Explanation:

$7 {x}^{2} - 10 x = - 3$

$7 {x}^{2} - 10 x + 3 = 0$

$\left(7 x - 3\right) \left(x - 1\right) = 0$

$7 x - 3 = 0$ or $x - 1 = 0$

$7 x = 3$ or $x = 1$

$x = \frac{3}{7}$ or $x = 1$

substitute x=3/7

$7 {\left(\frac{3}{7}\right)}^{2} - 10 \left(\frac{3}{7}\right) = - 3$

$7 \left(\frac{9}{7}\right) - \frac{30}{7} = - 3$

$\frac{63}{7} - \frac{30}{7} = - 3$

$\frac{33}{7} = - 3$

$4 \frac{4}{7} = - 3$

$x = \frac{3}{7}$= Extraneous solution

substitute $x = 1$

$7 {\left(1\right)}^{2} - 10 \left(1\right) = - 3$

$7 - 10 = - 3$

$- 3 = - 3$

$\therefore x = 1$