The most general proccedure for this type of problems is the following:
For a quadratic function of the following form
; 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: ![(\frac{b}{2})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7Bb%7D%7B2%7D%29%5E2)
3) Add and subtract in the function the value of ![(\frac{b}{2})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7Bb%7D%7B2%7D%29%5E2)
4) Write the complete function of the form
For the function presented
the result is as follows:
1) The value of b is 12
2) ![(\frac{12}{2} )^2=36](https://tex.z-dn.net/?f=%28%5Cfrac%7B12%7D%7B2%7D%20%29%5E2%3D36)
3) ![f(x)=(x^2+12x+36)-36+6](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E2%2B12x%2B36%29-36%2B6)
4)![f(x)=(x+6)^2-36+6](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B6%29%5E2-36%2B6)
Finally the function is:
![f(x)=(x + 6)^2-30](https://tex.z-dn.net/?f=f%28x%29%3D%28x%20%2B%206%29%5E2-30)
The zero pair that must be added is 36 and -36