Algebra 2 Completing the Square word problem (full question in description)

Question

The amount of horsepower needed to overcome a wind drag on a certain automobile is given by: H(s)=0.005s²+0.007s-0.031, where s is the speed of the car in miles per hour.

How much horsepower is needed to overcome the wind drag on this car if it is traveling 55 miles per hour?(Hint: Round to the nearest hundredth)

By completing the square, at what speed will the car need to use 225 horsepower to overcome the wind drag? (Hint: Leave in fraction form until the end, and then round to the nearest hundredth)

Answer 1

How much horsepower is needed to overcome the wind drag on this car if it is traveling 55 miles per hour?

H(s) = 0.005s² + 0.007s - 0.031

H(55) = 0.005(55)² + 0.007(55) - 0.031 = 15.125 + 0.385 - 0.031 = 15.479 = 15.48 HP

By completing the square, at what speed will the car need to use 225 horsepower to overcome the wind drag?

225 = 0.005s² + 0.007s - 0.031

0.005s² + 0.007s - 0.031 = 225

0.005s² + 0.007s = 225 + 0.031

0.005(s² + (0.007/0/005)s) = 225.031

s² + (0.007/0/005)s) = 225.031/0.005

s² + (7/5)s) = 45006.2

s² + (7/5)s) + (7/10)² = 225031/5 + (7/10)²

(s + 7/10)² = 225031/5 + 49/100

(s + 7/10)² = 4500620/100 + 49/100

(s + 7/10)² = 4500669/100

√(s + 7/10)² = ±√(4500669/100)

s + 0.70 = ±212.148

s = -0.70 ± 212.148

s = -0.70 + 212.148 or s = -0.70 - 212.148

s = 211.45 or s = -212.85

We can ignore the negative answer so s = 211.45 mph

Answer 2

For the first question, plug in 55 for s and you get H(s)=15.48 HP. See attached video for steps. For the second question plug in 225 for H(s) then follow the steps to complete the square. See attached video for the steps. Speed is a positive answer so ignore the negative solution. You should have 211.45mph as the solution.