If using the method of completing the square to solve the quadratic equation x^2-19x-3=0 which number would have to be added to "complete the square"? Answer Attemptiont of 2 square

To complete the square for the quadratic equation \(x^2 - 19x - 3 = 0\), we need to focus on the quadratic and linear terms: \(x^2 - 19x\).<br /><br />The general form of a quadratic expression is \(x^2 + bx\). To complete the square, we add and subtract \(\left(\frac{b}{2}\right)^2\), where \(b\) is the coefficient of \(x\).<br /><br />In this case, \(b = -19\). So, we calculate \(\left(\frac{-19}{2}\right)^2\):<br /><br />\[<br />\left(\frac{-19}{2}\right)^2 = \left(-\frac{19}{2}\right)^2 = \frac{361}{4}<br />\]<br /><br />Therefore, the number that needs to be added to complete the square is \(\frac{361}{4}\).