SOLUTION: what is the value of x in the equation: x-1/4 = 5/x+7

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Question 417641: what is the value of x in the equation:
x-1/4 = 5/x+7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-1%29%2F4=5%2F%28x%2B7%29 Start with the given equation.


%28x-1%29%28x%2B7%29=5%2A4 Cross multiply


%28x-1%29%28x%2B7%29=20 Multiply


x%5E2%2B6x-7=20 FOIL


x%5E2%2B6x-7-20=0 Subtract 20 from both sides.


x%5E2%2B6x-27=0 Combine like terms.


Notice that the quadratic x%5E2%2B6x-27 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=-27


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-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-27%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=-27


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-27%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36--108+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-27%29 to get -108


x+=+%28-6+%2B-+sqrt%28+36%2B108+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--108%29 as sqrt%2836%2B108%29


x+=+%28-6+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29 Add 36 to 108 to get 144


x+=+%28-6+%2B-+sqrt%28+144+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+12%29%2F%282%29 Take the square root of 144 to get 12.


x+=+%28-6+%2B+12%29%2F%282%29 or x+=+%28-6+-+12%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%28-18%29%2F%282%29 Combine like terms.


x+=+3 or x+=+-9 Simplify.


So the solutions are x+=+3 or x+=+-9


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