SOLUTION: I need help. Can't solve it. 3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000

Algebra ->  Equations -> SOLUTION: I need help. Can't solve it. 3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000       Log On


   

Question 1109273: I need help. Can't solve it.
3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000




Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I need help. Can't solve it.
3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000
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It's just a matter of being careful.
13(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2)) = 200000
48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2) = 200000/13
48x + x^2/6 + 2x*sqrt((x^2/4 + (x^2/36)) = 200000/13
48x + x^2/6 + 2x*sqrt((10x^2/36)) = 200000/13
48x + x^2/6 + 2x*(x/6)sqrt(10) = 200000/13
48x + x^2/6 + (x^2/3)sqrt(10) = 200000/13
x^2/6 + (2x^2/6)sqrt(10) + 48x = 200000/13
x^2*(2sqrt(10)+1)/6 + 48x - 200000/13 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1.22075922005613x%5E2%2B48x%2B-15384.6153846154+=+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=%2848%29%5E2-4%2A1.22075922005613%2A-15384.6153846154=77427.6443111465.

Discriminant d=77427.6443111465 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-48%2B-sqrt%28+77427.6443111465+%29%29%2F2%5Ca.




Quadratic expression 1.22075922005613x%5E2%2B48x%2B-15384.6153846154 can be factored:

Again, the answer is: 94.3094384866179, -133.629231621412. Here's your graph: