What number must be added to the polynomial to complete the square x2 13x?

Answer 1

Complete the square is the process of creating a "perfect square" polynomial.

We call (x + a)^2 a perfect square, where a is a constant. Using simple distributivity of numbers, we get

x^2 + 2ax + a^2 is a representation of a perfect square in simplified formed.

so (x + a) ^2 = x^2 + 2ax + a^2.

Given a degree polynomial in the form x^2 + nx, where m and n are constants, when we "complete the square", we are looking for values that will turn it into something like x^2 + 2ax + a^2. The entire idea is to find what "a" is.

2a is the coefficient for the degree one monomial "2ax" for what we want, also n is the coefficient for the degree one monomial "nx" for what we have. Then why don't we just say n = 2a for some a. To find a, it's obvious a = n/2.

We have the degree 2 term (x^2), degree 1 term (nx = 2 . n/2 .x). We need the constant of a^2. a^2 = (n/2)^2 = n^2 / 4.

In this case, n = 13.