How do you solve x^2 + 5x + 6 = 0  using the quadratic formula?

May 7, 2018

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

Explanation:

$\implies x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

for a quadratic of the form $a {x}^{2} + b x + c$.

We have $a = 1$, $b = 5$, and $c = 6$.

$x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \left(1\right) \left(6\right)}}{2 \left(1\right)}$

$x = \frac{- 5 \pm \sqrt{25 - 24}}{2}$

$x = \frac{- 5 \pm \sqrt{1}}{2}$

$x = \frac{- 5 \pm 1}{2}$

Hence,

$x = - \frac{6}{2} = - 3$
and
$x = - \frac{4}{2} = - 2$

I'm not sure why you wanted to use the quadratic formula, but you could just factor the quadratic:

${x}^{2} + 5 x + 6 = \left(x + 3\right) \left(x + 2\right) = 0$

$x + 3 = 0 \to x = - 3$
and
$x + 2 = 0 \to x = - 2$