If using the method of completing the square to solve the quadratic equation x ^ 2 - 9x + 38 = 0 which number would have to be added to "complete the square"?

Answer 1

To complete the square for the quadratic equation \( x^2 - 9x + 38 = 0 \), we start by focusing on the terms involving \( x \).

1. First, take the coefficient of \( x \), which is \(-9\), and divide it by 2: \[ \frac{-9}{2} = -\frac{9}{2} \]

2. Next, square this result: \[ \left(-\frac{9}{2}\right)^2 = \frac{81}{4} \]

This value, \(\frac{81}{4}\), is the number that needs to be added to complete the square.

Thus, to complete the square for the equation \( x^2 - 9x + 38 = 0 \), you would need to add \(\frac{81}{4}\) to the left side.