Respuesta :

We do completing the square as follows:

Write the equation in such a way that the constants are on one side. 
x^2 + 2x = 13

We add a number to both sides that will complete the square on the side which contains the variable x.
x^2 + 2x + 1 = 13 +1

We factor the side which contains the variable x.
(x+1)^2 = 14

Therefore, we should add 1 in order to complete the square from the given equation.

Answer:

The answer is 1

Step-by-step explanation:

In order to complete the square, you have to know the rule for expanding a square of a binomial.

The rule says:

Let [tex](a+b)^2[/tex] a square of a binomial in general

The square of any binomial produces the following three terms:

1.   The square of the first term of the binomial: [tex]a^2[/tex]

2.   Twice the product of the two terms:  [tex]2*a*b[/tex]

3.   The square of the second term: [tex]b^2[/tex]

So, the expand of a square of a binomial is:

[tex](a+b)^2=a^2+2*a*b+b^2[/tex]

Therefore, we should think which of the three terms mentioned before it is absent.

1. First term is [tex]x^2[/tex]

2. Second term is [tex]2*x[/tex]

3. Third term must be [tex]1[/tex] because it is the unique number which multiplying by [tex]x[/tex] results in [tex]2*x[/tex]

Finally, adding 1 in both side of the equation:

[tex]x^2+2*x+1=13+1\\(x+1)^2=14[/tex]

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