# How do you solve x^2 + 2x - 15 = 0 ?

Apr 12, 2018

$x = - 5 \text{ or } x = 3$

#### Explanation:

$\text{the factors of - 15 which sum to + 2 are + 5 and - 3}$

$\Rightarrow \left(x + 5\right) \left(x - 3\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x + 5 = 0 \Rightarrow x = - 5$

$x - 3 = 0 \Rightarrow x = 3$

Apr 12, 2018

$x = - 5 \mathmr{and} 3$

#### Explanation:

Rules for factorising:

• $a {x}^{2} + b x + c = 0$
• $m \times n = c$
• $m + n = b$
• $\therefore \left(x + m\right) \left(x + n\right) = 0$

In this case:

$5 \times - 3 = - 15 = c$

$5 + - 3 = 2 = b$

:. x^2+2x−15=0 -> color(red)((x+5)(x-3) = 0)

Either of the brackets must be equal to 0.

Assuming (x+5) = 0:

$\textcolor{red}{x = - 5}$

Assuming (x-3) = 0:

$\textcolor{red}{x = 3}$