The equation d=0.12v^2 + 2.1v models the distance d in feet it takes a car traveling at a speed of v miles per hour to come to a complete stop. Graces car was able to stop after 350ft on a highway. If the speed limit in the area was 35 miles per hour, was she speeding? Justify your answer.

Question

I did 350=0.12v^2 +2.1v
-350to both sides -350
0=0.12v^2 +2.1v-350
a=.12
b=2.1
c=-350
x=-b+- square root b^2-4ac/2a
x=-2.1+- square root 4.41-4(.12)(-350)/2(.12)

x=-2.1+- square root172.41/.24
square root of 172.41= 13.13, now divide that by .24=54.71
-2.1 +54.71 = 52.61
-2.1-54.71= -56.81 - we don't use this one
So if the speed limit was 35 mph , Grace was speeding, going approx. 52 mph

Can you please check my work? Is this correct?
Thank you for your help!!

Answer 1

It looks good most of the way; just a small error near the end:
First work out -2.1 + 13.13, and then divide the result by 0.24.
Same correction needed for your second solution.

Answer 2

thank you
so I got 45.95, so approx. 46mph, which is still over the speed limit.
Thank you for taking the time to check my long involved problem.