If using the method of completing the square to solve the quadratic equation x^2+13x+15=0 which number would have to be added to "complete the square"?

The number to be added to complete the square is (13/2) ^2

But the solved value for x are:

x = 11.71 or - 1.28

Step-by-step explanation:

x ^ 2 + 13x + 15 = 0

x^2 + 13x = - 15

(The coefficient of x^2 is 1, hence needless diving through)

Add the square of half the coefficient of x to both sides

x^2 + 13x + (13/2) ^2 = - 15 + (13/2) ^2

(x + 13/2) ^2 = - 15 + 169/4

(x + 13/2) ^2 = 109/4

Take the square of both sides

x + 13/2 = + -10.44 / 2

x = 10.44/2 + 13 / 2

x = 23.44/2

x = 11.71

OR

x = 10.44/2 - 13/2

x = - 2.56/2

x = - 1.28

Therefore x = 11.71 or - 1.28

But the number to be added to complete the square is (13/2) ^2

Lets keep learning, maths is fun