To solve the quadratic equation x^2 - 4x - 5 = 0, you can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 1, b = -4, and c = -5. Plug these values into the quadratic formula:
x = (-(-4) ± √((-4)² - 4(1)(-5))) / (2(1))
Simplify:
x = (4 ± √(16 + 20)) / 2
x = (4 ± √36) / 2
Now, calculate the two possible solutions:
1. x = (4 + 6) / 2 = 10 / 2 = 5
2. x = (4 - 6) / 2 = -2 / 2 = -1
So, the solutions to the quadratic equation x^2 - 4x - 5 = 0 are x = 5 and x = -1.