write as:
#y=3/7x^2+2/7x-4/7#..................................(1)
#y=3/7(x^2+color(blue)(2/3x))-4/7#
consider the #2/3" from "color(blue)( 2/3x)" and multiply it by "color(brown)( 1/2)#
#color(brown)(1/2)xxcolor(blue)(2/3)=color(green)(1/3)#
#y!=3/7(x+color(green)(1/3))^2-4/7" "##color(purple)(" This introduces an error!")#
Let #k# be some constant then:
#y=3/7(x+1/3)^2+k-4/7# ...................(2) #color(purple)("Corrected the error!")#
expanding to find the value of k
#y=3/7x^2+2/7x+1/21+k-4/7# ......................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equate equation (1) to equation (3) through y
#cancel(3/7x^2)+cancel(2/7x)-cancel(4/7)" "=" "cancel(3/7x^2)+cancel(2/7x)+1/21+k-cancel(4/7)#
#k+1/21=0" "->" "k=-1/21#.............................(4)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute (4) into (2) giving
#y=3/7(x+1/3)^2-1/21-4/7 ...................(2_a)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solution:
#y=3/7(x+1/3)^2-13/21#
#color(purple)("Please check the arithmetic. I can not spot any error but I am not")# #color(purple)("totally satisfied with the answer!")#
