Answer:
If we consider real numbers, there is no solution.
If we take into account imaginary numbers, there are 2 solutions. [tex]x=8i, -8i[/tex]
Step-by-step explanation:
We can take 64 to the other side and then take the square root.
Thus, we have:
[tex]x^2+64=0\\x^2=-64\\x=\sqrt{-64}[/tex]
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:
[tex]x=\sqrt{-64} \\x=\sqrt{(-1)(64)} \\x=\sqrt{-1} \sqrt{64} \\x=8i[/tex]
Where [tex]\sqrt{-1} =i[/tex]
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
