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Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general form of the quadratic equation is:
So lets solve
Plug in a=3, b=-2, and c=1
Square -2 to get 4
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 out
to make the radicand positive)
Multiply 2 and 3 to get 6
After simplifying, the quadratic has roots of
Notice if we graph the quadratic
, we get
we can see that the quadratic has no x-intercepts. This means there are no real solutions. So this verifies our answer.