Question 1152632
When solving - 3x^2 + 4x + 3 = 0 by completing the square, what would [x - (2/3)]^2 equal ?
<pre>{{{matrix(1,3, - 3x^2 + 4x + 3, "=", 0)}}}
{{{matrix(1,3,  -  3x^2 + 4x, "=", - 3)}}}
{{{matrix(1,3, - 3(x^2 - (4/3)x), "=", - 3(1))}}} 
{{{matrix(1,3, x^2 - (4/3)x, "=", 1)}}}
{{{matrix(1,3, x^2 - (4/3)x + ((1/2)  * (- 4/3))^2, "=", 1 + ((1/2) * (- 4/3))^2)}}} --- Taking {{{1/2}}} of b, squaring the result, then adding to both sides
{{{matrix(1,3, x^2 - (4/3)x + (- 2/3)^2, "=", 1 + (- 2/3)^2 )}}}
{{{matrix(1,3, (x  -  2/3)^2, "=", 1 + 4/9)}}}
{{{highlight_green(matrix(1,4, "Therefore,", (x - 2/3)^2, "=", 1&4/9))}}}