Solve the following equation: x^2 +36=0

Question

x=____
(Simplify your answer. Express complex numbers in terms of i. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Answer 1

To solve the equation \( x^2 + 36 = 0 \), we first isolate \( x^2 \):

\[ x^2 = -36 \]

Next, we take the square root of both sides. Since we are dealing with a negative number under the square root, we will introduce \( i \), the imaginary unit, which represents \( \sqrt{-1} \):

\[ x = \pm \sqrt{-36} \]

This can be simplified as follows:

\[ x = \pm \sqrt{36} \cdot \sqrt{-1} = \pm 6i \]

Thus, the solutions to the equation are:

\[ x = 6i, -6i \]

Therefore, the final answer is:

\[ 6i, -6i \]