Final answer:
The question seeks the value of 'c' for two quadratic equations using the quadratic formula, but the provided reference information is not directly applicable.
Step-by-step explanation:
The question is asking us to find the value of c that would satisfy two quadratic equations of the form q² + 10q + c and w² - 5w + c. Given the information, we need to apply the quadratic formula (-b ± √(b² - 4ac)) / (2a) to find the correct value of c that satisfies the conditions of both equations. Unfortunately, the reference information provided doesn't match the initial question's format, as they pertain to different equations with specified values for a, b, and c.