# How do you solve 25x ^ { 2} + 50x = 24?

Nov 5, 2017

$x = \frac{2}{5} , - \frac{12}{5}$

#### Explanation:

You can either use the quadratic formula or simply factor

Using factoring,
$25 {x}^{2} + 50 x - 24 = 0$
$\left(5 x - 2\right) \left(5 x + 12\right) = 0$

Therefore,
$5 x - 2 = 0$
$x = \frac{2}{5}$

$5 x + 12 = 0$
$x = - \frac{12}{5}$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 25 , b = 50 , c = - 24$

$x = \frac{- 50 \pm \sqrt{{50}^{2} - \left(4 \cdot 25 \cdot - 24\right)}}{2 \cdot 25}$

$x = \frac{- 50 \pm 70}{50}$

$x = \frac{- 50 + 70}{50}$
$x = \frac{2}{5}$

$x = \frac{- 50 - 70}{50}$
$x = - \frac{12}{5}$

Nov 5, 2017

$x = \frac{2}{5} \textcolor{w h i t e}{\text{xxx")"or"color(white)("xxx}} x = - 2 \frac{2}{5}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 25 {x}^{2} + 50 x = 24$

$25 \left({x}^{2} + 2 x\right) = 24$

$\textcolor{g r e e n}{25} \left({x}^{2} + 2 x \textcolor{m a \ge n t a}{+ 1}\right) = 24 \textcolor{m a \ge n t a}{+ 1} \times \textcolor{g r e e n}{25}$

$25 {\left(x + 1\right)}^{2} = 49$

${\left(x + 1\right)}^{2} = \frac{49}{25}$

$\left(x + 1\right) = \pm \frac{7}{5}$

$x = + \frac{7}{5} - 1 = \frac{2}{5} \textcolor{w h i t e}{\text{xxx")"or"color(white)("xxx}} x = - \frac{7}{5} - 1 = - \frac{12}{5} = - 2 \frac{2}{5}$