How do you solve the inequality #(x+6)^2 <=8#?

1 Answer
Jun 20, 2018

Answer:

#-6-2sqrt2<=x<= -6+2sqrt2#

Explanation:

#"subtract 8 from both sides"#

#(x+6)^2-8<=0#

#"solve "(x+6)^2-8=0#

#"using "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"with "a=x+6" and "b=sqrt8=2sqrt2#

#=(x+6-2sqrt2)(x+6+2sqrt2)=0#

#x+6-2sqrt2=0rArrx=-6+2sqrt2#

#x+6+2sqrt2=0rArrx=-6-2sqrt2#

#"since coefficient of "x^2>0" then minimum " uuu#

#-6-2sqrt2<=x<=-6+2sqrt2#
graph{(x+6)^2-8 [-16.02, 16.01, -8.01, 8.01]}