Question

If using the method of completing the square to solve the quadratic equation x^2+15x+7=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square, we need to add the square of half of the coefficient of x to both sides of the equation. In this case, the coefficient of x is 15, so we need to add (15/2)^2 = 225/4 to both sides of the equation.

x^2 + 15x + 7 = 0

x^2 + 15x + 225/4 = -7 + 225/4

(x + 15/2)^2 = - 193/4

So the number that needs to be added to complete the square is 225/4.