Given 3x^2 + x =1, find the value of 6x^3 - x^2 -3x + 2010

Question

radar · Answer

Solve the quadratic 3x^2+x-1=0
first I try factoring  well that didn't work so use the complete the square
dividing thru by 3 getting
x^2 + x/3 - 1/3= 0  add (1/6)^2
x^2 + x/3 + 1/36 = 1/3 +1/36
(x +1/6)^2 = 13/36       now take sq rt both sides
x +1/6 = sq rt (13/36)
$$x + 1/6 =\sqrt{13}/6$$
$$x=-(1/6)\pm1/6\sqrt{13}$$

radar · Answer

Can you solve for x, and then substitute those values in your 2nd equation?

radar · Answer

$$x=-(1/6)\pm(1/6)\sqrt{13}$$
That may be a little clearer.

anonymous · Answer

I will try to do the rest. Thanks...The Substitution part.

radar · Answer

Meantime I continue using calculator to get answer

radar · Answer

x=0.434 and x= -0.1

radar · Answer

I come up with 2009 and 2009.997 I know there is still another value but don't know how to solve for it.  I also think that those answers can not be trusted.