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

Jul 15, 2016

$\textcolor{b l u e}{x = 0}$ or $\textcolor{b l u e}{x = - 15}$

#### Explanation:

Factoring ${x}^{2} + 15 x = 0$
gives
$\textcolor{w h i t e}{\text{XX}} x \left(x + 15\right) = 0$

which implies
either
$\textcolor{w h i t e}{\text{XX}} x = 0$
or
$\textcolor{w h i t e}{\text{XX}} \left(x + 15 = 0\right)$
$\textcolor{w h i t e}{\text{XXXXX}} \rightarrow x = - 15$

Jul 15, 2016

$x = 0 , \mathmr{and} x = - 15$

#### Explanation:

The first approach is always to try and factorise the quadratic. Although this is not a trinomial, there is a common factor.

$x \left(x + 15\right) = 0$

Because the product is 0, one of the two factors must be equal to 0.

Either $x = 0 , \mathmr{and} x + 15 = 0 , \text{ in which case } x = - 15$

This gives two solutions, exactly what we expect with a quadratic.