Final answer:
The larger solution to the equation -x^2 + 6x + 5 = 0 lies between the consecutive integers -7 and -6, which is found by using the values in the quadratic formula.
Step-by-step explanation:
The given equation is -x^2 + 6x + 5 = 0. The quadratic formula is used to solve equations in the form ax^2 + bx + c = 0. For the given equation, a = -1, b = 6, and c = 5. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the values into the formula:
- x = (6 ± √((6)^2 - 4(-1)(5))) / (2(-1))
- x = (6 ± √(36 + 20)) / (-2)
- x = (6 ± √56) / (-2)
- x = (6 ± 7.483) / (-2)
Considering the larger solution, we have:
- x = (6 + 7.483) / (-2)
- x = 13.483 / (-2)
- x = -6.7415
This indicates that the larger solution to the equation lies between the consecutive integers -7 and -6.