SOLUTION: solve 2x^2-2x-1=0 by any method.

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Question 336365: solve 2x^2-2x-1=0 by any method.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-2x-1=0 Start with the given equation.


Notice that the quadratic 2x%5E2-2x-1 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-2, 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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-1%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-2, and C=-1


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


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


x+=+%282+%2B-+sqrt%28+4--8+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-1%29 to get -8


x+=+%282+%2B-+sqrt%28+4%2B8+%29%29%2F%282%282%29%29 Rewrite sqrt%284--8%29 as sqrt%284%2B8%29


x+=+%282+%2B-+sqrt%28+12+%29%29%2F%282%282%29%29 Add 4 to 8 to get 12


x+=+%282+%2B-+sqrt%28+12+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%282+%2B-+2%2Asqrt%283%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%283%29%29%2F%284%29 or x+=+%282-2%2Asqrt%283%29%29%2F%284%29 Break up the expression.


x+=+%281%2Bsqrt%283%29%29%2F%282%29 or x+=+%281-sqrt%283%29%29%2F%282%29 Reduce.


So the solutions are x+=+%281%2Bsqrt%283%29%29%2F%282%29 or x+=+%281-sqrt%283%29%29%2F%282%29


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

Also, feel free to check out my website.

Jim