Solve h=-49(t-2)^2+169.6

$$h = - 49 ( t - 2 ) ^ { 2 } + 169.6$$

Solve for h

$$h=-49\left(t-2\right)^{2}+169.6$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-2\right)^{2}.

$$h=-49\left(t^{2}-4t+4\right)+169.6$$

Use the distributive property to multiply -49 by t^{2}-4t+4.

$$h=-49t^{2}+196t-196+169.6$$

Add -196 and 169.6 to get -26.4.

$$h=-49t^{2}+196t-26.4$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{4240-25h}}{35}+2$$

$$t=\frac{\sqrt{4240-25h}}{35}+2$$

Solve for t

$$t=-\frac{\sqrt{4240-25h}}{35}+2$$

$$t=\frac{\sqrt{4240-25h}}{35}+2\text{, }h\leq \frac{848}{5}$$