Find all values of the variable $x$ for which the rational expression is undefined. \[ \frac{6 x+17}{x^{2}+14 x+40} \] The expression is undefined when $x=$

Step 1 ：The expression is undefined when the denominator equals zero. Therefore, we need to find the roots of the quadratic equation \(x^{2}+14 x+40=0\).

Step 2 ：Solving the quadratic equation, we find the roots to be -10 and -4.

Step 3 ：Final Answer: The rational expression is undefined when \(x\) equals to the roots of the quadratic equation in the denominator. Therefore, the values of \(x\) for which the expression is undefined are \(\boxed{-10}\) and \(\boxed{-4}\).