Question

Which of the following correctly completes the the square for the equation below? x^2+18x=0

Answer 1

We know that a perfect square has the form
(x+y)^2 = x^2+2xy+y^2
If we substitute the numbers in the given equation, we have
(x+y)^2 = x^2+2xy+y^2 = x^2+2x(9) + y^2
By comparison of the coefficients of the term xy, we have y=9, hence we need y^2=9^2=81 to complete the square.

The completed square would be
(x+9)^2-81=0 (which expands back to x^2+18x=0)

However, if the objective is to solve the equation, I would solve it by factoring, i.e.
x^2+18x=0 => x(x+18)=0 => x=0 or x=-18

Answer 2

x² +18x = 0

To complete the square we are going to use formula a² +2ab +b² = (a+b)²

x² +2*9*x = 0
x² +2*9x+9² = 9²
(x+9)² = 9²
√(x+9)² = +/-√9²
x+9 = 9, or x+9 = -9
x=0, or x= - 18

The equation could be solved different way
x² +18x = 0
x(x+18) = 0
x=0 or x+18=0
x=0 or x=-18