# How do you solve x^2+5x+6=0 by factoring?

Jul 16, 2018

$x = - 3 \text{ or } x = - 2$

#### Explanation:

$\text{the factors of "+6" which sum to "+5}$
$\text{are "+3" and } + 2$

$\left(x + 3\right) \left(x + 2\right) = 0$

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

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

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

Jul 16, 2018

$x = - 2$ or $x = - 3$

#### Explanation:

Completing the square

${x}^{2} + 2 \cdot \frac{5}{2} x + \frac{25}{4} + 6 - \frac{25}{4} = 0$

we get

${\left(x + \frac{5}{2}\right)}^{2} - \frac{1}{4} = 0$

using that ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

we get
$\left(x + \frac{5}{2} - \frac{1}{2}\right) \left(x + \frac{5}{2} + \frac{1}{2}\right) = 0$

so $\left(x + 2\right) \left(x + 3\right) = 0$

we get $x = - 2$ or $x = - 3$

Jul 16, 2018

$x = - 2$ and $x = - 3$

#### Explanation:

Let's do a little thought experiment:

What two numbers sum to the middle term, and have a product of the last term?

After some trial and error, we arrive at $2$ and $3$. This means we can factor this as

$\left(x + 2\right) \left(x + 3\right) = 0$

Next, we can set both factors equal to zero to get

$x = - 2$ and $x = - 3$

Hope this helps!