Question

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

Answer 1

`-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]}