SOLUTION: I have to use the quadratic formula to solve this equation. I have successfully completed my 15 other problems and checked my work. For some reason this problem is giving me the bl

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to use the quadratic formula to solve this equation. I have successfully completed my 15 other problems and checked my work. For some reason this problem is giving me the bl      Log On


   

Question 642382: I have to use the quadratic formula to solve this equation. I have successfully completed my 15 other problems and checked my work. For some reason this problem is giving me the blues. Can someone please help me with this and show me step by step on how to do it. I also have to present my final solutions as decimal approximations carried out to the third decimal place. Thank you in advance I greatly appreciate it.
1/2x^2+x=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29x%5E2%2Bx=1

x%5E2%2B2x=2 Multiply EVERY term by the LCD 2 to clear out the fraction.

x%5E2%2B2x-2=0

Now use the quadratic formula to solve for x

Note: x%5E2%2B2x-2 really looks like and it is in the form ax%5E2%2Bbx%2Bc where a = 1, b = 2 and c = -2


x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%282%29%2B-sqrt%28%282%29%5E2-4%281%29%28-2%29%29%29%2F%282%281%29%29

x+=+%28-2%2B-sqrt%284-%28-8%29%29%29%2F%282%29

x+=+%28-2%2B-sqrt%284%2B8%29%29%2F%282%29

x+=+%28-2%2B-sqrt%2812%29%29%2F2

x+=+%28-2%2Bsqrt%2812%29%29%2F2 or x+=+%28-2-sqrt%2812%29%29%2F2

x+=+%28-2%2B2%2Asqrt%283%29%29%2F2 or x+=+%28-2-2%2Asqrt%283%29%29%2F2

x+=+-1%2Bsqrt%283%29 or x+=+-1-sqrt%283%29

x+=+0.732050807568877 or x+=+-2.73205080756888

So the exact solutions are x+=+-1%2Bsqrt%283%29 or x+=+-1-sqrt%283%29

and the approximate solutions are x+=+0.732050807568877 or x+=+-2.73205080756888

These approximate solutions round to x+=+0.732 or x+=+-2.732

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Final Answer:

x+=+0.732 or x+=+-2.732
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Jim
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