To complete the square for the polynomial \( h^2 - 7h \), we need to find the number that makes it a perfect-square quadratic.
-
Start with the expression: \( h^2 - 7h \).
-
Take the coefficient of \( h \) (which is -7), divide it by 2, and then square the result:
\[ \left(-\frac{7}{2}\right)^2 = \frac{49}{4} \]
-
This means we need to add \( \frac{49}{4} \) to complete the square.
Therefore, the expression becomes:
\[ h^2 - 7h + \frac{49}{4} \]
Now, the expression \( h^2 - 7h + \frac{49}{4} \) can be written as a perfect square:
\[ \left(h - \frac{7}{2}\right)^2 \]
So the number to fill in the blank is \( \frac{49}{4} \).
1 answer