SOLUTION: Hi, i cant seem to solve (8/x)+(108/x^2)=96.88 ^2 = squared Can anybody help me with this please?

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Question 174691: Hi, i cant seem to solve (8/x)+(108/x^2)=96.88
^2 = squared
Can anybody help me with this please?
Found 3 solutions by Alan3354, stanbon, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, i cant seem to solve (8/x)+(108/x^2)=96.88
-------------
Multiply thru by x^2
8x + 108 = 96.88x^2
Divide by 4, and put in standard form
24.22x^2 - 2x - 27 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 24.22x%5E2%2B-2x%2B-27+=+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=%28-2%29%5E2-4%2A24.22%2A-27=2619.76.

Discriminant d=2619.76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+2619.76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+2619.76+%29%29%2F2%5C24.22+=+1.09792714947549
x%5B2%5D+=+%28-%28-2%29-sqrt%28+2619.76+%29%29%2F2%5C24.22+=+-1.01535076632107

Quadratic expression 24.22x%5E2%2B-2x%2B-27 can be factored:
24.22x%5E2%2B-2x%2B-27+=+%28x-1.09792714947549%29%2A%28x--1.01535076632107%29
Again, the answer is: 1.09792714947549, -1.01535076632107. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+24.22%2Ax%5E2%2B-2%2Ax%2B-27+%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve (8/x)+(108/x^2)=96.88
^2 = squared
I think you garbled your posting.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Fx%2B108%2Fx%5E2=96.88 Start with the given equation.


x%5E2%288%2Fcross%28x%29%29%2Bx%5E2%28108%2Fcross%28x%5E2%29%29=96.88x%5E2 Multiply EVERY term by the LCD x%5E2 to clear out the fractions.


8x%2B108=96.88x%5E2 Simplify


800x%2B10800=9688x%5E2 Multiply both sides by 100 to make every number a whole number.


-9688x%5E2%2B800x%2B10800=0 Subtract 9688x%5E2 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-9688, b=800, and c=10800


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


Plug in a=-9688, b=800, and c=10800


x+=+%28-800+%2B-+sqrt%28+640000-4%28-9688%29%2810800%29+%29%29%2F%282%28-9688%29%29 Square 800 to get 640000.


x+=+%28-800+%2B-+sqrt%28+640000--418521600+%29%29%2F%282%28-9688%29%29 Multiply 4%28-9688%29%2810800%29 to get -418521600


x+=+%28-800+%2B-+sqrt%28+640000%2B418521600+%29%29%2F%282%28-9688%29%29 Rewrite sqrt%28640000--418521600%29 as sqrt%28640000%2B418521600%29


x+=+%28-800+%2B-+sqrt%28+419161600+%29%29%2F%282%28-9688%29%29 Add 640000 to 418521600 to get 419161600


x+=+%28-800+%2B-+sqrt%28+419161600+%29%29%2F%28-19376%29 Multiply 2 and -9688 to get -19376.


x+=+%28-800+%2B-+80%2Asqrt%2865494%29%29%2F%28-19376%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-800%2B80%2Asqrt%2865494%29%29%2F%28-19376%29 or x+=+%28-800-80%2Asqrt%2865494%29%29%2F%28-19376%29 Break up the expression.


So the answers are x+=+%28-800%2B80%2Asqrt%2865494%29%29%2F%28-19376%29 or x+=+%28-800-80%2Asqrt%2865494%29%29%2F%28-19376%29


which approximate to x=-1.015 or x=1.098