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How do you solve #-(x+2)^2<=0#?

Answer 1

Avery Alexander

#x in RR#

There are two methods we can do this:

#:. x in RR#

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

Multiply by #-1#:

#(x+2)^2<=0#

Take each side's square root:

#pm(x+2)<=0#

#x<=-2#

#-x-2<=0#

#-x<=2#

#x>=-2#

#-2<=x<=-2, :. x in RR#

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Answer 2

Kennedy Adams

We can validate this with a sketch:

We see its always negative

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Answer 3

Isaiah Anthony

To solve the inequality ( -(x+2)^2 \leq 0 ), you need to find the values of ( x ) that make the expression less than or equal to zero. This inequality holds true when ( x ) is between negative infinity and negative two, inclusive. So, the solution is ( x \leq -2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #-(x+2)^2&lt;=0#?

How do you solve #-(x+2)^2<=0#?