If using the method of completing the square to solve the quadratic equation x^2+15x+25=0x

2

+15x+25=0, which number would have to be added to "complete the square"?

x = - 15/2 ± (1/2) * 5√5

Step-by-step explanation:

I will assume that you meant x^2+15x+25=0.

To complete the square, take half of the coefficient of x, square the result, add this square into the equation after '15x,' and then subtract the square from the result:

x^2+15x+25=0 = > x^2 + 15x + (15/2) ^2 - (15/2) ^2 + 25 = 0.

Rewrite the first two terms as (x + 15/2) ^2 - 225/4 + 100/4 = 0, or

(x + 15/2) ^2 - 125/4 = 0

Taking the square root of both sides, we obtain the solutions:

x + 15/2 ±√[125/4], or

x = - 15/2 ± (1/2) * 5√5