How do you solve x( 5x - 2) = 24?

May 1, 2018

$x = \frac{12}{5} \mathmr{and} 2.4 , - 2$

Explanation:

expand:

$x \left(5 x - 2\right) \to 5 {x}^{2} - 2 x = 24$

set equal to $0$:

$5 {x}^{2} - 2 x = 24 \to 5 {x}^{2} - 2 x - 24 = 0$

factorise:

$\to 5 {x}^{2} + 10 x - 12 x - 24$

$\to 5 x \left(x + 2\right) - 12 \left(x + 2\right)$

$\Rightarrow \left(x + 2\right) \left(5 x - 12\right)$

Check to see if correct:

$\left(5 x - 12\right) \left(x + 2\right) = 5 {x}^{2} + 10 x - 12 x - 24$

$\to 5 {x}^{2} - 2 x - 24$.

set each bracket equal to $0$:

$5 x - 12 = 0$

$\to 5 x = 12$

$\Rightarrow x = \frac{12}{5}$

$x + 2 = 0$

$\Rightarrow x = - 2$

Check these values:

$2.4 \left(5 \times 2.4 - 2\right) = 2.4 \times 10 = 24$

$- 2 \left(5 \times - 2 - 2\right)$=-2 xx -12=24#

$\therefore$ these values are correct.