Question 180630
You want to find x so that C(x)=11500.
{{{C(x)=0.5x^2+15x+5000=11500}}}
{{{0.5x^2+15x-6500=0}}}
{{{x^2+30x-13000=0}}}
In other words, find the zeros of this quadratic equation and you'll have your solution.
You can factor this equation or use the quadratic formula to solve it.
{{{(x+130)(x-100)=0}}}
We'll only solve for the positive solution since the negative solution in this case doesn't make sense.
{{{x-100=0}}}
{{{highlight(x=100)}}}