Question

How do you solve the quadratic `x^2+x=-1` using any method?

Answer 1

Use the quadratic formula to find roots:

`-1/2+-sqrt(3)/2i`

Explanation:

If you add `1` to both sides, the equation becomes:

`x^2+x+1=0`

This is in the form `ax^2+bx+c = 0` with `a = b = c = 1`.

This has roots given by the quadratic formula:

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`=(-1+-sqrt(1^2-4(1)(1)))/(2*1)`

`=(-1+-sqrt(-3))/2`

`=-1/2+-sqrt(3)/2i`