How do you solve #x^2+6x+9>=0# using a sign chart?

1 Answer
Dec 23, 2016

Answer:

The answer is #x in RR#

Explanation:

We use

#(a+b)^2=a^2+2ab+b^2#

Factorise the expression

#x^2+6x+9=(x+3)^2#

Let #f(x)=(x+3)^2#

The domain of #f(x)# is #D_f(x)=RR#

and

#AA x in RR#, #f(x)>=0#

So,

#x in RR#

The sign chart is simple

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x+3##color(white)(aaaa)##-##color(white)(aaa)##0##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaa)##0##color(white)(aa)##+#

Therefore,

#f(x)>=0# when #x in RR#