The quadratic equation by completing the square x^2+6x=18

This technique is valid only when the coefficient of x2 is 1.

1) Transpose the constant term to the right

x2 + 6x = - 2.

2) Add a square number to both sides - - add the square of half the coefficient of x. In this case, add the square of half of 6; that is, add the square of 3, which is 9:

x2 + 6x + 9 = - 2 + 9.

The left-hand side is now the perfect square of (x + 3).

(x + 3) 2 = 7.

3 is half of the coefficient 6.

That equation has the form

a2 = b which implies a = ±. Therefore, x + 3 = ± x = - 3 ±.

That is, the solutions to

x2 + 6x + 2 = 0