SOLUTION: Please help me solve this equation: 2/x-x/8=3/4

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Question 195570This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: 2/x-x/8=3/4 This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Fx-x%2F8=3%2F4 Start with the given equation.


Multiply every term on both sides by the LCD 8x. Doing this will eliminate all of the fractions.


8%282%29-x%28x%29=2x%283%29 Cancel out and simplify


16-x%5E2=6x Multiply


16-x%5E2-6x=0 Get all terms to the left side.


-x%5E2-6x%2B16=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=-6, and c=16


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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%28-1%29%2816%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=-6, and c=16


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%28-1%29%2816%29+%29%29%2F%282%28-1%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%28-1%29%2816%29+%29%29%2F%282%28-1%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36--64+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%2816%29 to get -64


x+=+%286+%2B-+sqrt%28+36%2B64+%29%29%2F%282%28-1%29%29 Rewrite sqrt%2836--64%29 as sqrt%2836%2B64%29


x+=+%286+%2B-+sqrt%28+100+%29%29%2F%282%28-1%29%29 Add 36 to 64 to get 100


x+=+%286+%2B-+sqrt%28+100+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%286+%2B-+10%29%2F%28-2%29 Take the square root of 100 to get 10.


x+=+%286+%2B+10%29%2F%28-2%29 or x+=+%286+-+10%29%2F%28-2%29 Break up the expression.


x+=+%2816%29%2F%28-2%29 or x+=++%28-4%29%2F%28-2%29 Combine like terms.


x+=+-8 or x+=+2 Simplify.


So the answers are x+=+-8 or x+=+2