SOLUTION: x/2 = 5/x + 3

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Question 201522: x/2 = 5/x + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F2++=+5%2F%28x+%2B+3%29 Start with the given equation.


x%28x+%2B+3%29++=+2%2A5 Cross multiply


x%5E2%2B3x=+2%2A5 Distribute


x%5E2%2B3x=10 Multiply


x%5E2%2B3x-10=0 Subtract 10 from both sides.


Notice that the quadratic x%5E2%2B3x-10 is 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-%283%29+%2B-+sqrt%28+%283%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+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--40+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-10%29 to get -40


x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F%282%281%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 9 to 40 to get 49


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-3+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%28-3+%2B+7%29%2F%282%29 or x+=+%28-3+-+7%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-10%29%2F%282%29 Combine like terms.


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


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