Multiply out the racket giving:" "6x^2-5x=6
Subtract 6 from both sides
" "6x^2-5x-6=0
Write as" "6(x^2-5/6x)-6=0
Take the square outside the bracket and add the correction constant k
6(x-5/6x)^2-6+k=0
Remove the x from -5/6x
6(x-5/6)^2-6+k=0
Multiply the -5/6 by (1/2)
6(x-5/(12))^2-6+k=0
'~~~~~~~~~~~~~ Comment ~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the part of (x-5/12)(x-5/12)
The (-5/12)^2 is an introduced value that is not in the original equation so we remove it by subtraction. However, this introduced error is in fact 6(-5/12)^2 due to the 6 outside the brackets
=>k=(-1)xx6xx(-5/12)^2= -1 1/24 =-25/24
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(brown)(6(x-5/(12))^2-6+k=0)" "->" "color(blue)(6(x-5/(12))^2-6-25/24=0
=>6(x-5/(12))^2-169/24=0
6(x-5/12)^2=169/24
(x-5/12)^2=169/144
Taking the square root of both sides
x-5/12=+-sqrt(169)/sqrt(144) = +-13/12
x=5/12+-13/12
x=+18/12" and " -8/12
x=+3/2" and " -2/3
