SOLUTION: How do you figure out how to solve {{{(x-3)/2=5/x}}}?

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Question 343583: How do you figure out how to solve %28x-3%29%2F2=5%2Fx?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%2F2=5%2Fx Start with the given equation.


x%28x-3%29=5%2A2 Cross multiply.


x%28x%29-x%283%29=5%2A2 Distribute.


x%5E2-3x=10 Multiply


x%5E2-3x-10=0 Subtract 10 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-3, and c=-10


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


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-3, and c=-10


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--40+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-10%29 to get -40


x+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%281%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 9 to 40 to get 49


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%283+%2B+7%29%2F%282%29 or x+=+%283+-+7%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+5 or x+=+-2 Simplify.


So the answers are x+=+5 or x+=+-2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I know how to solve it, but I'm not sure I know how to figure out how to solve it. It is just something I know.

Cross-multiply, collect all of the terms in the LHS so that everything is set equal to zero, then solve the resulting easily factorable quadratic equation. Note that you will have two roots. Check both of them.

John

My calculator said it, I believe it, that settles it