How do I solve the formula #16t^2 - vt - 40 = 0# for #t#?
1 Answer
Jun 16, 2018
# t = (v +-sqrt(v^2+2560))/32 #
Explanation:
We have:
# 16t^2-vt-40 = 0 #
We can complete the square, by first dividing by the coefficient of
# :. 16{t^2-v/16t-40/16} = 0 #
# :. t^2-v/16t-5/2 = 0 #
Then we factor half the coefficient of
# :. (t-v/32)^2-(v/32)^2-5/2 = 0 #
Which we can now readily rearrange for
# :. (t-v/32)^2 = v^2/1024+5/2 #
# :. (t-v/32)^2 = v^2/1024+2560/1024 #
# :. (t-v/32)^2 = (v^2+2560)/1024 #
# :. t-v/32 = +-sqrt((v^2+2560)/1024) #
# :. t-v/32 = +-sqrt(v^2+2560)/32 #
# :. t = v/32 +-sqrt(v^2+2560)/32 #
# :. t = (v +-sqrt(v^2+2560))/32 #