SOLUTION: Formula D=0.054^2+0.058x describes the distance in feet D that it takes a vehicle traveling x mph to stop on dry pavement. A. How fast can you drive if you wish to be able to

Question 536385: Formula D=0.054^2+0.058x describes the distance in feet D that it takes a vehicle traveling x mph to stop on dry pavement.
A. How fast can you drive if you wish to be able to stop within 65 feet?
I have it started with 0.054x^2+0.058x=65. How do I proceed from here?? Please help!
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
You have a quadratic equation, almost in standard form to solve. Change:
.054x^2 + .058x = 65 to the standard form by subtracting 65 from both sides:
...
.054x^2 + .058x - 65 = 0
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The next step in solving quadratic equations like this is to factor the equation then solve for the X value(s) that let the equation = 0
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Note: it will be easier to manipulate the equation by getting the coefficient for the x^2 term = 1. Do that by dividing everything by .054:
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x^2 + .058/.054 - 65/.054 = 0
x^2 + 1.074x - 1203.704 = 0
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This factors to:
(x + 35.235) * (x - 34.162) = 0
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x = -35.235 or x = 34.162
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x = -35.235 mph doesn't make any sense, so reject that possible solution. The one remaining is the correct answer.
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x = 34.162 mph is the max speed to travel to be able to stop in 65 feet. Note: this result is an approximation (there are actually several decimal places involved, but in practical terms of driving an automobile, they seem irrelevant). 8-)
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Happy Thanksgiving!
Lee
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