Question

Find the value of c that completes the square

x^2-16x+c

Please help me with how to do this, and show me. Thank you.

Answer 1

The value that completes the square is: c=8

Explanation:

Find the value of c that completes the square
`x^2-16x+c`

The formula used is:
`a^2-2ab+b^2=(a-b)^2`

In the question given the value c can be found by breaking the middle term. we are given -16x while the general formula is 2ab for middle term so,

2(x)(8) = 16x

so, c= 8

Solving:

`x^2-16x+c\\=x^2-2(x)(8)+(8)^2-(8)^2\\=(x-8)^2-64`

So, the value that completes the square is: c=8