SOLUTION: 1-13/x+36/x^2=0

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Question 186687: 1-13/x+36/x^2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1-13%2Fx%2B36%2Fx%5E2=0 Start with the given equation.


x%5E2-13x%2B36=0 Multiply EVERY term by the LCD x%5E2 to clear out the fractions.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-13, and c=36


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-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%2836%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-13, and c=36


x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%2836%29+%29%29%2F%282%281%29%29 Negate -13 to get 13.


x+=+%2813+%2B-+sqrt%28+169-4%281%29%2836%29+%29%29%2F%282%281%29%29 Square -13 to get 169.


x+=+%2813+%2B-+sqrt%28+169-144+%29%29%2F%282%281%29%29 Multiply 4%281%29%2836%29 to get 144


x+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 144 from 169 to get 25


x+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2813+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


x+=+%2813+%2B+5%29%2F%282%29 or x+=+%2813+-+5%29%2F%282%29 Break up the expression.


x+=+%2818%29%2F%282%29 or x+=++%288%29%2F%282%29 Combine like terms.


x+=+9 or x+=+4 Simplify.


So the solutions are x+=+9 or x+=+4