Final answer:
To solve the quadratic equation x^2-7x-6=0, we apply the quadratic formula and find the two solutions to be x = (7 + √(73))/2 and x = (7 - √(73))/2.
Step-by-step explanation:
The quadratic equation x^2-7x-6=0 can be solved using the quadratic formula, which is x = (-b ± √(b^2-4ac))/(2a) for a quadratic equation in the form ax^2+bx+c = 0. In this equation, a = 1, b = -7, and c = -6.
Using these values, we get the following steps:
- Calculate the discriminant: √((-7)^2 - 4*1*(-6)) = √(49 + 24) = √(73)
- Apply the quadratic formula:
- x = (-(-7) ± √(73)) / (2*1)
- x = (7 ± √(73)) / 2
Thus, the two solutions for x are x = (7 + √(73))/2 and x = (7 - √(73))/2.
This gives us the two possible values for x.