The most general proccedure for this type of problems is the following:
For a quadratic function of the following form [tex]f(x)=x^2+bx+c[/tex]; where b and c are real numbers.
1) Identify the value that accompanies the x, that is, the value "b"
2) Divide the value of b by 2 and then square it: [tex](\frac{b}{2})^2[/tex]
3) Add and subtract in the function the value of [tex](\frac{b}{2})^2[/tex]
4) Write the complete function of the form [tex]f(x) = (x+\frac{b}{2})^2-(\frac{b}{2} )^2+c[/tex]
For the function presented [tex]f(x)=x^2 +12x+6[/tex] the result is as follows:
1) The value of b is 12
2) [tex](\frac{12}{2} )^2=36[/tex]
3) [tex]f(x)=(x^2+12x+36)-36+6[/tex]
4)[tex]f(x)=(x+6)^2-36+6[/tex]
Finally the function is:
[tex]f(x)=(x + 6)^2-30[/tex]
The zero pair that must be added is 36 and -36
