SOLUTION: 3x^2 -6x +1=0

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Question 629850: 3x^2 -6x +1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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3x%5E2-6x%2B1=0 Start with the given equation.


Notice that the quadratic 3x%5E2-6x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-6, 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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-6, and C=1


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%283%29%281%29+%29%29%2F%282%283%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%283%29%281%29+%29%29%2F%282%283%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-12+%29%29%2F%282%283%29%29 Multiply 4%283%29%281%29 to get 12


x+=+%286+%2B-+sqrt%28+24+%29%29%2F%282%283%29%29 Subtract 12 from 36 to get 24


x+=+%286+%2B-+sqrt%28+24+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%286+%2B-+2%2Asqrt%286%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%2B2%2Asqrt%286%29%29%2F%286%29 or x+=+%286-2%2Asqrt%286%29%29%2F%286%29 Break up the expression.


x+=+%283%2Bsqrt%286%29%29%2F%283%29 or x+=+%283-sqrt%286%29%29%2F%283%29 Reduce.


So the solutions are x+=+%283%2Bsqrt%286%29%29%2F%283%29 or x+=+%283-sqrt%286%29%29%2F%283%29

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