Given:#" "y=3x^2-30x-72#

Let #k# be the correction canstant

Write as;#" "y=3(x^(color(magenta)(2))-30/3x)-72+k#

Move the power of #color(magenta)(2)# to outside the bracket

#y=3(x-30/3color(green)(x))^(color(magenta)(2))-72+k#

Remove the #color(green)(x)# from #30/3x#

#y=3(x-30/3)^2 -72+k#

Apply #1/2xx(-30/3) = 30/6 = 5#

#y=3(x-5)^2 -72+k#

For the correction to work it has to be the case that

#color(red)(3)xx(-5)^2+k=0" "=>" "k=-75#

#color(red)("(do not forget to multiply by the value outside the brackets)")#

#y=3(x-5)^2 -72-75#

#y=3(x-5)^2 -147#