Question

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

Answer 1

Write your equation as:
`x^2-x+1=0` (taking `-1` to the right and changing sign)
now your equation is in the form: `ax^2+bx+c=0` where the numerical coefficients are:
`a=1`
`b=-1`
`c=1`
You can use them into the Quadratic Formula given as:
`x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)`
So:
`x_(1,2)=(1+-sqrt(1-4(1*1)))/(2)`
`x_(1,2)=(1+-sqrt(-3))/(2)`
The negative argument of your square root cannot give you a real number.
The solutions of your equation will be two Complex Numbers .
You can write:
`x_(1,2)=(1+-sqrt(-1*3))/(2)`
`x_(1,2)=(1+-isqrt(3))/(2)` where `i=sqrt(-1)`