# Question #d15b1

Oct 16, 2017

see explanation

#### Explanation:

I'm going to interpret the request to "solve" the equations as "find the roots".
For quadratic equations, we can plug the coefficients into the well known forumula

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

w(t) is a quadratic equation, with coefficients -3, 0, and 5. The roots are 1.29 and -1.29

For the second part, I guess you can substitute (-2-t) in for the t parameter in the equation.

So, you'd have:

$- 3 {\left(- 2 - t\right)}^{2} + 5$ giving:

$- 3 \left(4 + 4 t + {t}^{2}\right) + 5$

$= - 12 - 12 t - 3 {t}^{2} + 5$

$= - 3 {t}^{2} - 12 t - 7$

This is also a quadratic equation, with coefficients -3, -12, and -7. So you can solve for the roots, though we're not asked to do this. The roots are:

-3.29 and -0.71 (rounding)

GOOD LUCK