algebra 2 question read description

Question

A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approximated by d = 0.04v² + 0.5v,

 where v is the speed of the car. If the driver must be able to stop within 75 ft, what is the maximum safe speed, to the nearest mile per hour, of the car?

Answer 1

.04v² +.5v = 75

4v² _{+ 50v - 7500 = 0}

_{v =[-50 + sqrt(2500+120000)]/8}

_{(Note: the other root does not make physical sense)}

_{The approximate solution is a bit more than 30 mph...but I will leave the arithmetic to you.}