# How do you solve using the quadratic formula for h(t) = -0.5t^2 + 10t + 22?

Mar 14, 2018

Using the quadratic formula, the solutions for $a {x}^{2} + b x + c = 0$ are

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

So, we got here:

$a = - 0.5 , b = 10 , c = 22$

Therefore,

$t = \frac{- 10 \pm \sqrt{100 - 4 \cdot - 0.5 \cdot 22}}{-} 1$

$= \frac{- 10 \pm \sqrt{100 + 44}}{-} 1$

$= \frac{- 10 \pm \sqrt{144}}{-} 1$

$= \frac{- 10 \pm 12}{-} 1$

$= - \left(- 10 \pm 12\right)$

$= - \left(2 , - 22\right)$

$= - 2 , 22$

So, the solutions for $t$ will be $t \in \left\{- 2 , 22\right\}$.