Question

What is the solution for x^2+64=0​

Answer 1

So the answer would be 8i and -8i

Answer 2

If we consider real numbers, there is no solution.

If we take into account imaginary numbers, there are 2 solutions.
`x=8i, -8i`

Explanation:

We can take 64 to the other side and then take the square root.

Thus, we have:

`x^2+64=0\\x^2=-64\\x=√(-64)`

We CANNOT take the square root of a negative number, so there is no solution.

BUT, if we take into account Imaginary Numbers, we can solve:

`x=√(-64) \\x=√((-1)(64)) \\x=√(-1) √(64) \\x=8i`

Where
`√(-1) =i`

AND, we can take the positive and negative versions of 8i, since squaring would take it back to original.

So the answer would be 8i and -8i