For what real values of a is x^2 + ax + 25 the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.

If you could help me, that would be great!

what is -10, and +10

Thanks!

To determine the real values of 'a' for which the expression x^2 + ax + 25 is the square of a binomial, we can use the concept of completing the square.

A binomial squared usually follows the pattern (x + b)^2 = x^2 + 2bx + b^2.

In the given expression, the constant term is 25. So, in order for x^2 + ax + 25 to be a perfect square, the coefficient of 'x' (which is 'a') must be twice the square root of 25.

Therefore, we need to find values of 'a' for which a = 2√25 or a = ±10.

Hence, the real values of 'a' for which x^2 + ax + 25 is the square of a binomial are a = -10 and a = 10.

In increasing order, the answer is -10, 10.