the set S={x|x^2+4x-5=0}

The set S is defined as {x | x^2 + 4x - 5 = 0}. To understand what this set represents, we need to find the values of x that satisfy the equation x^2 + 4x - 5 = 0.

To solve this equation, we can use the quadratic formula, which states that for any equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

In our equation, a = 1, b = 4, and c = -5. We can substitute these values into the quadratic formula:

x = (-4 ± sqrt(4^2 - 4(1)(-5)))/(2(1))

Simplifying further:

x = (-4 ± sqrt(16 + 20))/2

x = (-4 ± sqrt(36))/2

x = (-4 ± 6)/2

This gives us two possible solutions:

x = (-4 + 6)/2 = 1

x = (-4 - 6)/2 = -5

Therefore, the set S consists of the values x = 1 and x = -5, since these are the solutions to the equation x^2 + 4x - 5 = 0. So, the set S = {1, -5}.