Question

What number must you add to the polynomial below to complete the square?X^2-26x

Answer 1

To complete the square, we should do these steps

1. Divide the middle term by 2 to find the product of the 1st and the 2nd terms of the bracket

2. find the square root of the 1st term

3. divide the product of them by the 1st term to find the 2nd term

4. Square the 2nd term, it will be the missing term in the polynomial

Let us do these steps

Since the 2nd term is -26x, then

1.

`-(26x)/(2)=-13x`

2.

`\sqrt[]{x^2}=x`

3.

`(-13x)/(x)=-13`

The 2nd term in the bracket is -13, then the bracket is

`(x-13)^2`

4.

`(-13)^2=169`

Then we should add 169 to the polynomial to make it the complete of the square

`x^2-26x+169=(x-13)^2`