Question

How do you solve `x(x+2)+3=0` by completing the square?

Answer 1

`0 = x(x+2)+3 = x^2 + 2x + 3 = (x+1)^2+2`. Subtracting 2 from both sides, we get `(x+1)^2 = -2`. If you square any real number you will get a positive value, so there are no real solutions to the problem.