Let f (x) be a quadratic equation of the form:
[tex]x^2+bx+c\\[/tex]
Where b and c are real numbers.
So a generic procedure for completing squares is:
1) identify b
In this case b = 10
2) divide b between 2 and then square it
[tex](\frac{b}{2})^ 2\\[/tex]
[tex](\frac{10}{2})^ 2=25\\[/tex]
3) Add and subtract [tex]b ^ 2[/tex] in the equation
[tex]x ^2+10x + 25 - 25 = 50\\[/tex]
[tex]x ^ 2 + 10x +25 = 75\\[/tex]
4) Rewrite the equation as follows
[tex](x+\frac{b}{2})^2=c\\[/tex]
[tex](x + 5) ^ 2 = 75\\[/tex]
The number that you must add to both sides of the equation is number [tex]25 = (\frac{b}{2})^2[/tex]
