SOLUTION: Solve the equation 2x + 5 = -1/x

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Question 336170: Solve the equation 2x + 5 = -1/x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x+%2B+5+=+-1%2Fx Start with the given equation.


2x%5E2+%2B+5x+=+-1 Multiply both EVERY term by the LCD x to clear out the fractions.


2x%5E2+%2B+5x+%2B1=+0 Add 1 to both sides.


Notice that the quadratic 2x%5E2%2B5x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=2, B=5, and C=1


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%282%29%281%29+%29%29%2F%282%282%29%29 Plug in A=2, B=5, and C=1


x+=+%28-5+%2B-+sqrt%28+25-4%282%29%281%29+%29%29%2F%282%282%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25-8+%29%29%2F%282%282%29%29 Multiply 4%282%29%281%29 to get 8


x+=+%28-5+%2B-+sqrt%28+17+%29%29%2F%282%282%29%29 Subtract 8 from 25 to get 17


x+=+%28-5+%2B-+sqrt%28+17+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-5%2Bsqrt%2817%29%29%2F%284%29 or x+=+%28-5-sqrt%2817%29%29%2F%284%29 Break up the expression.


So the solutions are x+=+%28-5%2Bsqrt%2817%29%29%2F%284%29 or x+=+%28-5-sqrt%2817%29%29%2F%284%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim