Question 1119035

if 3x^2-2x+7=0, then (x-1/3)^2=

A. 20/9
B. 7/9
C. -7/9
D. -8/9
E. -20/9

(im studying for college)
<pre>{{{matrix(1,3, 3x^2 - 2x + 7, "=", 0)}}}
{{{matrix(1,3, 3x^2 - 2x, "=", - 7)}}} -------- Subtracting 7 from both sides
{{{matrix(1,3, 3x^2/3 - (2/3)x, "=", - 7/3)}}} ----- Dividing by 3 to make the leading coefficient, 1 
{{{matrix(1,3, x^2 - (2/3)x, "=", - 7/3)}}}
{{{matrix(1,3, x^2 - (2/3)x + ((1/2) * (- 2/3))^2, "=", - 7/3 + ((1/2) * (- 2/3))^2)}}}  ------ Completing the square on x
{{{matrix(1,3, x^2 - (2/3)x + (- 1/3)^2, "=", - 7/3 + (- 1/3)^2)}}}
{{{matrix(1,3, (x - 1/3)^2, "=", - 7/3 + 1/9)}}}
{{{matrix(1,3, (x - 1/3)^2, "=", - 21/9 + 1/9)}}}
{{{highlight_green(matrix(1,3, (x - 1/3)^2, "=", highlight(- 20/9)))}}} (CHOICE E)