# How do you find the zeros, real and imaginary, of y=x^2+32x+44 using the quadratic formula?

Dec 24, 2015

Substitute the coefficients into the quadratic formula to find:

$x = - 16 \pm 2 \sqrt{53}$

#### Explanation:

${x}^{2} + 32 x + 44$ is of the form $a {x}^{2} + b x + c$
with $a = 1$, $b = 32$ and $c = 44$.

This has zeros given by the quadratic formula:

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

$= \frac{- 32 \pm \sqrt{{32}^{2} - \left(4 \times 1 \times 44\right)}}{2 \cdot 1}$

$= \frac{- 32 \pm \sqrt{1024 - 176}}{2}$

$= \frac{- 32 \pm \sqrt{848}}{2}$

$= \frac{- 32 \pm \sqrt{{4}^{2} \cdot 53}}{2}$

$= \frac{- 32 \pm 4 \sqrt{53}}{2}$

$= - 16 \pm 2 \sqrt{53}$