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How do you find the missing value to complete the square #x^2+2x#?

Answer 1

Genesis Allen

#(x+a)^2 = x^2+2ax+a^2#

We want #2ax# to match #2x#, so #a=1# and the missing value is #a^2 = 1^2 = 1#

#x^2+2x+1 = (x+1)^2#

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Answer 2

Jameson Allen

To complete the square for the expression ( x^2 + 2x ), follow these steps:

Take half of the coefficient of ( x ), square it, and add it to the expression.
Rewrite the expression as a perfect square trinomial.
Factor the perfect square trinomial.
Simplify the expression.

Here are the steps:

Take half of the coefficient of ( x ): ( \frac{2}{2} = 1 ).
Square it: ( 1^2 = 1 ).
Add it to the expression: ( x^2 + 2x + 1 ).
Rewrite the expression as a perfect square trinomial: ( (x + 1)^2 ).

So, ( x^2 + 2x ) can be completed as ( (x + 1)^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.