How do solve #x^2+6x>=0# and write the answer as a inequality and interval notation?

1 Answer
Nov 24, 2016

Answer:

The solutions are #x<=-6# and #x>=0#

or #x in] -oo,-6 ] uu [0, oo[ #

Explanation:

Let #f(x)=x^2+6x#

Let's factorise the equation

#x^2+6x=x(x+6)#

The values when #f(x)=0# are #x=0# and ##x=-6

Let's do a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-6##color(white)(aaaaa)##0##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x##color(white)(aaaaaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##x+6##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#

Therefore #f(x)>=0#
when, #x<=-6# and #x>=0#

#x in] -oo,-6 ] uu [0, oo[ #

graph{x^2+6x [-20.27, 20.27, -10.14, 10.14]}