Solve \( x^{2}=54 \), where \( x \) is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click "No solution." \( x=\square \)

To solve the equation \( x^{2} = 54 \), you start by taking the square root of both sides. This gives you: \[ x = \pm \sqrt{54} \] Now, simplify \( \sqrt{54} \). The number 54 can be factored into \( 9 \times 6 \), and since \( 9 \) is a perfect square, you can simplify further: \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6} \] Thus, the solutions are: \[ x = 3\sqrt{6}, -3\sqrt{6} \] So the final answer is: \( x = 3\sqrt{6}, -3\sqrt{6} \)