# How do you find the solution to the quadratic equation  0 = x^2 + 5x + 6?

Jun 20, 2018

x=-2 or -3

#### Explanation:

${x}^{2} + 5 x + 6 = 0$

${x}^{2} + 2 x + 3 x + 6 = 0$

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

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

$x = - 2 \mathmr{and} - 3$

Jun 20, 2018

$x = - 3 , x = - 2$

#### Explanation:

Lets factorise:

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

Check this is correct...

${x}^{2} + 3 x + 2 x + 6$

$\Rightarrow {x}^{2} + 5 x + 6 = 0$

Now solve:

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

$\therefore$ $x = - 3$

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

$\therefore$ $x = - 2$

Jun 21, 2018

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

#### Explanation:

Are there any two numbers that sum to the middle term ($5$), and have a product of the last term ($6$)?

After some trial and error, we arrive at

$2$ and $3$. Thus, we can factor the right side of our quadratic as

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

Setting both of our factors equal to zero, we get

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

Hope this helps!