Question

What number must you add to complete the square? x2 + 2x = 13

Answer 1

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 $(a+b)^2$ 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: $a^2$

2.   Twice the product of the two terms:  $2*a*b$

3.   The square of the second term: $b^2$

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

$(a+b)^2=a^2+2*a*b+b^2$

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

1. First term is $x^2$

2. Second term is $2*x$

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

Finally, adding 1 in both side of the equation:

$x^2+2*x+1=13+1\\(x+1)^2=14$

Answer 2

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.