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

Question 89339: solve
3x^2-2x+1=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=-2, and c=1

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: since we cannot take the square root of a negative value, we must factor to to make the radicand positive. If you need help with simplifying the square root, check out this solver)

Multiply 2 and 3 to get 6

After simplifying, the quadratic has roots of

or

Notice if we graph the quadratic , we get

graph of

To visually verify the answer, check out this page to see a visual representation of imaginary roots

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