# How do you factor and solve x^2 + 3x + 2 = 0?

May 21, 2018

$x = - 2$

#### Explanation:

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

${x}^{2} + 3 x = - 2$

A squared number + $3 x$ = negative 2 ($- 2$)

So $x$ must be negative.

$- {2}^{2} + \left(3 x - 2\right) = - 2$

$4 \pm 6 = - 2$

$x = - 2$

May 21, 2018

$x = - 2 \text{ or } x = - 1$

#### Explanation:

$\text{the factors of + 2 which sum to + 3 are + 2 and + 1}$

$\Rightarrow \left(x + 2\right) \left(x + 1\right) = 0$

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

$x + 2 = 0 \Rightarrow x = - 2$

$x + 1 = 0 \Rightarrow x = - 1$

$\text{solutions are "x=-2" or } x = - 1$