Question

What number needs added to complete the square:
x^2+18x+?

Answer 1

divide the coefficient of x by 2 then square it:-
coefficient of x = + 18 so we have
x^2 + 18x + 81 ( = (x + 9)^2 )

the requred number is 81

Answer 2

There is a plus sign where the constant is, meaning both factors will have positive signs. The variable with the coefficient of eighteen will mean there is a difference of half eighteen (this is because the two x factors will be added to make that 18x). 18/2=9.
Now we plug in the nine and create (x + 9)(x + 9). Then we use F.O.I.L.
First: x * x = x^2
Outer: x * 9 = +9x
Inner: x * 9 = +9x
Last: 9 * 9 = 81
Added together and put in order you have obtained x^2 + 18x + 81.
Conclusion: The coefficient is 81.