Question

How do you complete the square to solve `x^2 + 6x + 34 = 0`?

Answer 1

`x^2+6x+34 = 0`
can be written as
`color(white)("XXXX")` `x^2+6x = -34`

completing the square:
`color(white)("XXXX")` `x^2+6x+9 = -25`
`color(white)("XXXX")` `(x+3)^2 = -25`
take the square root of both sides
`color(white)("XXXX")` `x+3 = sqrt(-25)` `color(white)("XXXX")`(Note: no Real solutions)

`color(white)("XXXX")` `x= -3 +-5i`