For this case we have a polynomial of the form:
\(x ^ 2 + 12x = 11
\)
To complete the square, we must add on both sides of the equation a term of the form:
\((\frac{b}{2}) ^ 2
\)
Where,
b: coefficient of the exponent term equal to 1
We have then that for this case, completing squares:
\(x ^ 2 + 12x + (\frac{12}{2}) ^ 2 = 11 + (\frac{12}{2}) ^ 2
\)
Rewriting we have:
\(x ^ 2 + 12x + (6) ^ 2 = 11 + (6) ^ 2
x ^ 2 + 12x + 36 = 11 + 36
\)
Answer:
The number that should be added to both sides of the equation to complete the square is:
36
