what number needs to be added to both sides of the equation in order to complete the square

Question

x^2 + 14x=-32 is the problem

Answer 1

49.

You take the coefficient of x, diveide by two then square that value

Answer 2

I'm using area.

(x^2+14x)^2=-32^2

x^4+28x^3+196x^2=1024

x=2

Answer 3

If you want to complete the square for this, then you have to add the square of half of the coefficient of the x to the power of 1 to both sides.

In this case:

c = (14/2)^2 = 7^2 = 49

Add 49 to both sides.