Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

t2 − 19t +

Answer 1

To complete the square for the quadratic expression \( t^2 - 19t \), you'll want to find a number that makes this a perfect square trinomial.

The process involves taking half of the coefficient of \( t \), squaring it, and then adding it to the expression.

1. Take the coefficient of \( t \), which is \(-19\).
2. Half of \(-19\) is \(-\frac{19}{2}\).
3. Squaring this gives:
\[
\left(-\frac{19}{2}\right)^2 = \frac{361}{4}.
\]

Now we add this value to \( t^2 - 19t \) to complete the square:

\[
t^2 - 19t + \frac{361}{4}.
\]

Thus, the completed square form is:

\[
\left(t - \frac{19}{2}\right)^2.
\]

So, the number that needs to be added to make the polynomial a perfect-square quadratic is \( \frac{361}{4} \).