Expert: Steve Holleran - 9/30/2007

Question
Hello Mr Holleran, I've tried to solve this equation 3x2-2x-6=0 by completing by square but couldn't find a conclusive answer. Can you help me please and show me every step and how to check the answer.
Thank you

Answer
Hi Henoc,

Okay, to complete the square here, let's first divide through the equation by 3:

     3x^2 - 2x - 6 = 0 ----> x^2 - 2/3 x - 2 = 0

Now move the -2 over:    x^2 - 2/3 x     = 2

Okay, we take half the linear coefficient, 2/3, which is 1/3, and square it: 1/9.  Add this to both sides:

            x^2 - 2/3 x + 1/9 = 2 + 1/9 = 19/9

Now write the left side as a binomial squared:

             (x - 1/3)^2 = 19/9

Take sq. rt:    (x - 1/3) = +/- sqrt(19/9)

then                   x = 1/3 +/- sqrt(19/9)

or                     x = 1/3 +/- sqrt(19) / 3

if you want, you can write:  x = (1 +/- sqrt(19))/ 3

I hope this is what you needed.

Steve