8. If using the method of completing the square to solve the quadratic equation x^2-14x-40=0 which number would have to be added to "complete the square"?

To complete the square for the quadratic equation \(x^2 - 14x - 40 = 0\), we need to focus on the quadratic and linear terms: \(x^2 - 14x\).<br /><br />The coefficient of \(x\) is \(-14\). To complete the square, we take half of this coefficient and then square it. Here are the steps:<br /><br />1. Take half of the coefficient of \(x\):<br /> \[<br /> \frac{-14}{2} = -7<br /> \]<br /><br />2. Square this value:<br /> \[<br /> (-7)^2 = 49<br /> \]<br /><br />So, the number that needs to be added to complete the square is \(49\).