Quadratic formula equation question

G

Guest

Guest
This is the quadratic formula I'm using
78.26x^2+55113.04x+45007.77

The question is using algebra (the quadratic formula) to determine when seminole county florida will have a population of 500,000

I have no I idea where to begin, I haven't taken algebra in a year...If this isn't enough information I could just write down the whole problem if someone can't figure that out. Thank you.
 
At a guess,
\(\displaystyle \mbox{P(x) = 78.26x^2 + 55113.04x + 45007.77}\)
models the population \(\displaystyle \mbox{P(x)}\) after \(\displaystyle \mbox{x}\) years (although this does mean the population is growing rather quickly).

To determine after how many years, that is \(\displaystyle \mbox{x}\), the population reaches 500,000, we would set \(\displaystyle \mbox{P(x) = 500,000}\):

\(\displaystyle \mbox{ 500,000 = 78.26x^2 + 55113.04x + 45007.77}\)

Rearrange into the form \(\displaystyle \mbox{ax^2 + bx + c = 0}\):

\(\displaystyle \mbox{ 78.26x^2 + 55113.04x - 454992.23 = 0}\)

And apply the quadratic formula:

\(\displaystyle \Huge \mbox{ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\)

to solve for \(\displaystyle \mbox{x}\):

\(\displaystyle \Huge \mbox{ x = \frac{-55113.04 \pm sqrt{55113.04^2 - 4\times78.26\times(-454992.23)}}{2\times78.26}}\)

You can reject a negative value of \(\displaystyle \mbox{x}\) (and be left with just the positive one).
 
Assuming what you wrote is an equation and = the population
And you know when
ax²+bx+c = 0
x=(-b ± sqrt(b²-4ac)/2a
You have only to set it equal to 500,000 and solve for x.

Hint:
a=78.26
b=55113.04
c=(45007.77 - 500000)

BTW: If you worked up the equation I would suggest t or y (time or year) would have been a better variable than x. When you get done it is nice if the variable suggests what it stands for. If they gave it to you, never mind.
 
quadratic problem

the answer im getting is 50.28, is that right ?...thanks again
 
You can check a solution by plugging that value for x into the original equation.

I get x = 8.16 approx as the positive solution.
 
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