Complete the Square: Fill in the Blanks for (x+?)^2 = x^2 + ? + 25

To solve this problem, we'll use the formula for the square of a sum, $(a+b)^2 = a^2 + 2ab + b^2$. This will help us determine the missing components in the expression.

The expression given is $(x+?)^2 = x^2 + ? + 25$.

First, match it to the expanded form:

$(x+b)^2 = x^2 + 2bx + b^2$.

According to the problem, the expanded form is $x^2 + ? + 25$. This means $b^2 = 25$, so:
$b^2 = 25$
Therefore, $b = 5$ or $b = -5$. For simplicity, let's choose $b = 5$.

Now, calculate $2bx$:
$2bx = 2 \times 5 \times x = 10x$

Substituting $b$ into the equation, we have:

$(x+5)^2 = x^2 + 10x + 25$.

Thus, the missing numbers are $5$ and $10x$.

Therefore, the solution to the problem is $5, 10x$.