Question

Find the value of c that completes the square

x^2+2x+c

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

Answer 1

The value of c that completes the square
`x^2+2x+c` is 1

Explanation:

We need to find the value of c that completes the square
`x^2+2x+c`

The formula used will be:
`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 2x while the general formula is 2ab for middle term so,

2(x)(1) = 2x

so, c= 1

Solving:

`x^2+2x+c\\=x^2+2(x)(1)+(1)^2-(1)^2\\=(x+1)^2-1`

So, the value of c that completes the square
`x^2+2x+c` is 1