Question

How do you solve `x^2-2x+7=-4` using the quadratic formula?

Answer 1

`x=1+-isqrt10`

(There are no real solutions.)

Explanation:

Make one side equal to zero by adding 4 to each side:
`x^2-2x+7=-4`
`x^2-2x+11=0`

Quadratic formula:
`x=(-b+-sqrt(b^2-4ac))/(2a)`
`x=(2+-sqrt[(-2)^2-(4)(1)(11)])/(2*1)`

Simplify:
`x=(2+-sqrt(-40))/(2)`
`x=(2+-2isqrt10)/2`
`x=1+-isqrt10`