To complete the square for the polynomial \( h^2 - 10h + __ \), we need to find a number to add that will make the expression a perfect square.
The general formula for completing the square for a quadratic expression in the form \( h^2 + bh \) is to take half of the coefficient \( b \) of \( h \), square it, and add it to the expression.
In your case, the coefficient \( b \) is \(-10\).
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Take half of \(-10\): \[ \frac{-10}{2} = -5 \]
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Square it: \[ (-5)^2 = 25 \]
So, the number that makes the polynomial a perfect-square quadratic is \( 25 \).
Thus, the completed expression is:
\[ h^2 - 10h + 25 \]
This can be factored as:
\[ (h - 5)^2 \]
So, the number you fill in is 25.
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