Answer:
The value of c that completes the square [tex]x^2+2x+c[/tex] is 1
Step-by-step explanation:
We need to find the value of c that completes the square [tex]x^2+2x+c[/tex]
The formula used will be: [tex]a^2+2ab+b^2=(a+b)^2[/tex]
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:
[tex]x^2+2x+c\\=x^2+2(x)(1)+(1)^2-(1)^2\\=(x+1)^2-1[/tex]
So, the value of c that completes the square [tex]x^2+2x+c[/tex] is 1
