Question

How do you solve `x^2-x= -1` using the quadratic formula?

Answer 1

`1/2+-isqrt(3)/2`

Explanation:

We need to solve the equation as standard form (`ax^2+bx+c`):

`x^2-x+1=0`

The quadratic formula states that `(-color(red)(b))/(2(color(blue)(a))) +-sqrt(color(red)(b)^2-4 xx color(blue)(a) xx color(green)(c))/(2(color(blue)(a)))`:

`(-(color(red)(-1)))/(2(color(blue)(1))) +-sqrt((color(red)(-1))^2-4 xx color(blue)(1) xx color(green)(1))/(2(color(blue)(1)))`

`1/2 +- sqrt(1-4)/2`

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

`1/2+-isqrt(3)/2 = x`