Greg, are you sure the equation is x²+216=0, with addition? If that's the right equation, then subtracting 216 from both sides yields x²= -216. This equation has no real solutions, because you can't square a real number and get a negative number. But it does have two complex solutions, namely plus or minus the square root of -216, which is plus or minus i*(the square root of 216).

If, however, the equation was supposed to be x² -216=0, with subtraction instead of addition, then we can add 216 to both sides to get x²=216, so that x would be plus or minus the square root of 216, as you said. If you're confused about what the square root of 216 is, you can either (a) use a calculator to approximate it to any desired number of decimal places, or (b) simplify the square root of 216 by looking for factors that are perfect squares. A moment's thought shows you that 216=36*6, so the square root of 216 is the same as (square root of 36)*(square root of 6), but the square root of 36 is 6, so we just get 6*(square root of 6). If you don't immediately recognize that 216 is divisible by 36, you can try looking for smaller perfect squares like 4 and 9 first; you'll just have to simplify in more than one step.

Does this answer whatever question you had?

Matt

B.S. Theoretical Mathematics, MIT

Well Greg, thanks for asking.

x^2 + 216 = 0

Step by step solving we get:
x^2 + 216 = 0
squareroot(x^2 + 216) = squareroot (0)
sqrt(x^2) + sqrt(216) = 0
x + sqrt(216) = 0
x = -sqrt(216)

I hope this helps :)