Question 130296
The last day of ticket sales will correspond to the rightmost zero. So we need to find the zeros




{{{y=-0.2x^2+12x+11}}} Start with the given equation



{{{0=-0.2x^2+12x+11}}} Set y equal to zero



{{{10(0)=10(-0.2x^2+12x+11)}}} Multiply both sides by 10 to get rid of the decimal number



{{{0=-2x^2+120x+110}}} Distribute and multiply 



Let's use the quadratic formula to solve for x:



Starting with the general quadratic


{{{ax^2+bx+c=0}}}


the general solution using the quadratic equation is:


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}}




So lets solve {{{-2*x^2+120*x+110=0}}} ( notice {{{a=-2}}}, {{{b=120}}}, and {{{c=110}}})





{{{x = (-120 +- sqrt( (120)^2-4*-2*110 ))/(2*-2)}}} Plug in a=-2, b=120, and c=110




{{{x = (-120 +- sqrt( 14400-4*-2*110 ))/(2*-2)}}} Square 120 to get 14400  




{{{x = (-120 +- sqrt( 14400+880 ))/(2*-2)}}} Multiply {{{-4*110*-2}}} to get {{{880}}}




{{{x = (-120 +- sqrt( 15280 ))/(2*-2)}}} Combine like terms in the radicand (everything under the square root)




{{{x = (-120 +- 4*sqrt(955))/(2*-2)}}} Simplify the square root (note: If you need help with simplifying the square root, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)




{{{x = (-120 +- 4*sqrt(955))/-4}}} Multiply 2 and -2 to get -4


So now the expression breaks down into two parts


{{{x = (-120 + 4*sqrt(955))/-4}}} or {{{x = (-120 - 4*sqrt(955))/-4}}}



Now break up the fraction



{{{x=-120/-4+4*sqrt(955)/-4}}} or {{{x=-120/-4-4*sqrt(955)/-4}}}



Simplify



{{{x=30-sqrt(955)}}} or {{{x=30+sqrt(955)}}}



So these expressions approximate to


{{{x=-0.903074280724887}}} or {{{x=60.9030742807249}}}



So our solutions are:

{{{x=-0.903074280724887}}} or {{{x=60.9030742807249}}}




So the last day of ticket sales will be on the 60th day