SOLUTION: This has been asked before and Stan was the one who responded. I can see where he was going, but I don't like to just take an answer, I like to figure it out, too and see where I

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: This has been asked before and Stan was the one who responded. I can see where he was going, but I don't like to just take an answer, I like to figure it out, too and see where I       Log On


   

Question 257229: This has been asked before and Stan was the one who responded. I can see where he was going, but I don't like to just take an answer, I like to figure it out, too and see where I go. I am not getting the same answer, so I was wondering if someone can tell me where I am going wrong. Here is what I have been doing:
PROBLEM:
Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).

And when it comes to figuring out the last day of sales, I do this:
- .2x^2+12x+11
a= -.2 b= 12 c= 11
x= -(-.2)+- sqrt(12^2-4*(-.2)*11/2*(-.2)
x= .2 +- sqrt(144-(-.8)*11/-.4
x= .2 +- sqrt(144-(-8.8)/-.4
x= .2 +- sqrt(152.8)/-.4
And this is where I get lost.....I am getting decimals out the rear and can't figure out what I am doing wrong. Does this even look close??? I would really, really appreciate any help.... I'm about to give up... It's been 2 days working on this stupid problem. Ugh!!
Found 2 solutions by Alan3354, drk:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Was Stan's answer correct? Can you copy and paste what he did?
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I'll start with your quadratic:
- .2x^2+12x+11
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.2x%5E2%2B12x%2B11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A-0.2%2A11=152.8.

Discriminant d=152.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+152.8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+152.8+%29%29%2F2%5C-0.2+=+-0.903074280724887
x%5B2%5D+=+%28-%2812%29-sqrt%28+152.8+%29%29%2F2%5C-0.2+=+60.9030742807249

Quadratic expression -0.2x%5E2%2B12x%2B11 can be factored:
-0.2x%5E2%2B12x%2B11+=+%28x--0.903074280724887%29%2A%28x-60.9030742807249%29
Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2%2Ax%5E2%2B12%2Ax%2B11+%29

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The graph is off the page, but the solver does the calculations.
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Email via the thank you note with any questions.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
So it appears you were given this or somehow you cam up with this
-+.2x%5E2%2B12x%2B11
Either way I assume this is correct.
We apply the quadratic as
x+=+%28-12+%2B-+sqrt%28+144-4%2A%28-.2%29%2A%2811%29+%29%29%2F%28-.4%29+
and then
x+=+%28-12+%2B-+sqrt%28+152.8+%29%29%2F%28-.4%29+
which is
x+=+60.90307
or
x+=+-.90307
The average of these 2 is 30.
The vertex formula is
y+=+-.2%28x-30%29%5E2+%2B+198
at 30 days, you sell 198 tickets.