Question

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

Answer 1

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 impliesa = ±.         Therefore,x + 3 = ± x = −3 ±.

That is, the solutions to

x2 + 6x + 2  =  0