Question 739436
The formula D=0.054x^2+0.058x describes the distance in feet that it takes to stop a vehicle traveling x miles per hour on dry pavement.
How fast can you drive if you wish to be able to stop your car within 65 feet?
:
.054x^2 + .058x = 65
A quadratic equation
.054x^2 + .058x - 65 = 0
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation, a=.054, b=.058, c=-65
{{{x = (-.058 +- sqrt(.058^2-4*.054*-65 ))/(2*.054) }}}
:
{{{x = (-.058 +- sqrt(.003364+14.04 ))/(.108) }}}
:
{{{x = (-.058 +- sqrt(14.04673 ))/(.108) }}}
the positive solution is all we want here
{{{x = (-.058 + 3.7479)/(.108) }}} 
x = {{{3.69/.108}}}
x = 34.167 mph for a stopping distance of 65 ft