Match the following equation with its solutions. \[ x^{2}=45 \]

Step 1 ：The given equation is \(x^{2}=45\).

Step 2 ：To find the solutions, we need to take the square root of both sides.

Step 3 ：However, we need to remember that the square root of a number is both positive and negative.

Step 4 ：Therefore, the solutions to the equation will be both positive and negative square root of 45.

Step 5 ：The positive solution is \(\sqrt{45}\) which is approximately 6.708203932499369.

Step 6 ：The negative solution is \(-\sqrt{45}\) which is approximately -6.708203932499369.

Step 7 ：Final Answer: The solutions to the equation \(x^{2}=45\) are \(\boxed{6.708203932499369}\) and \(\boxed{-6.708203932499369}\).