Question

What is the solution for x^2+64=0​

Answer 1

Answer:

If we consider real numbers, there is no solution.

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

Step-by-step explanation:

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

Thus, we have:

$x^2+64=0\\x^2=-64\\x=\sqrt{-64}$

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:

$x=\sqrt{-64} \\x=\sqrt{(-1)(64)} \\x=\sqrt{-1} \sqrt{64} \\x=8i$

Where $\sqrt{-1} =i$

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

Answer 2

Answer:

So the answer would be 8i and -8i