Solving a Simple Quadratic Problem: 3x^2 - 12x + 11 with the Quadratic Formula

[BuBbLeS01]

Homework Statement

I am trying to use the quadratic formula for 3x^2 - 12x +11 and I am getting...
12 +/- (sqrt 12)/6 which is supposed to reduce to 6 +/- (sqrt 3)/3 and I can't figure it out...it's very sad!

 

[rock.freak667]

$$\sqrt{12} = \sqrt{4*3}= \sqrt{4}\sqrt{3} =2\sqrt{3}$$

 

[symbolipoint]

The 2/2 cancels, involving the distributive property.

You did not use grouping symbols correctly in your message, but see the steps:

((2*2*3) +/- (2*2*3)^(.5))/(2*3)
=((2*2*3) +/- (2)*(3^(0.5)))/(2*3)
= 2*(2*3 +/- (3^(0.5)))/(2*3)
Notice the factor of 2 in numerator and factor of 2 in denominator; you need to write these steps longhand so you can see clearly; no typesetting system here on my end...
... simplifies quite well to
=(2*3 +/- (3^(0.5)))/3
=(6 +/- (3^(0.5))/3

Also watch my work carefully in case I make any grouping symbol error. I just caught a few that I corrected, but again check carefully.

 

[BuBbLeS01]

$$\sqrt{12} = \sqrt{4*3}= \sqrt{4}\sqrt{3} =2\sqrt{3}$$

So you have (12 * 2 * sqrt 3) / 6 which simplifies to (6 * 1 * sqrt3) / 3 then to
(6 * sqrt 3) / 3