0=70-4t-16t² based on your previous questions, you should have learned how to complete the square
solve by copmleting the square
minus 70 both sides -70=-4t-16t² times both sides by -1 70=4t+16t² 16t²+4t=70 divide both sides by 16 t²+1/4t=35/8 take 1/2 of the linear coefint and square it half of 1/4=1/8, (1/8)²=1/64 add that to both sides t²+1/4t+1/64=35/8+1/64 factor perfect square trionomial [tex](t+\frac{1}{8})^2=\frac{35}{8}+\frac{1}{64}[/tex] [tex](t+\frac{1}{8})^2=\frac{280}{64}+\frac{1}{64}[/tex] [tex](t+\frac{1}{8})^2=\frac{281}{64}[/tex] square root both sides, remember to take positive and negative roots [tex]t+\frac{1}{8}=\frac{+/-\sqrt{281}}{8}[/tex] minus 1/8 [tex]t=\frac{-1+/-\sqrt{281}}{8}[/tex]
[tex]t=\frac{-1+\sqrt{281}}{8}[/tex] or [tex]t=\frac{-1-\sqrt{281}}{8}[/tex] the 2nd solution is not valid because that gives us a negative time, before the ball was dropped
so [tex]t=\frac{-1+\sqrt{281}}{8}[/tex] is the solution t≈1.97
