Question

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

Answer 1

The answer is 1

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.