SOLUTION: Solve 3x^2-6x+1=0 using the quadratic formula.

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Question 869565: Solve 3x^2-6x+1=0 using the quadratic formula.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve 3%2Ax%5E2-6%2Ax%2B1=0 ( notice a=3, b=-6, and c=1)





x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29 Plug in a=3, b=-6, and c=1




x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29 Negate -6 to get 6




x+=+%286+%2B-+sqrt%28+36-4%2A3%2A1+%29%29%2F%282%2A3%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)




x+=+%286+%2B-+sqrt%28+36%2B-12+%29%29%2F%282%2A3%29 Multiply -4%2A1%2A3 to get -12




x+=+%286+%2B-+sqrt%28+24+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%286+%2B-+2%2Asqrt%286%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%286+%2B-+2%2Asqrt%286%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%286+%2B+2%2Asqrt%286%29%29%2F6 or x+=+%286+-+2%2Asqrt%286%29%29%2F6



Now break up the fraction



x=%2B6%2F6%2B2%2Asqrt%286%29%2F6 or x=%2B6%2F6-2%2Asqrt%286%29%2F6



Simplify



x=1%2Bsqrt%286%29%2F3 or x=1-sqrt%286%29%2F3



So the solutions are:

x=1%2Bsqrt%286%29%2F3 or x=1-sqrt%286%29%2F3