Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators.
\[
5 x^{2}=55
\]
The solution set is $\{3.31\}$.
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Express imaginary solutions in the form $a+b i$.)
Answer
Final Answer: The solution set is \(\boxed{\{3.3166247903554, -3.3166247903554\}}\).
Step 1 ：Given the equation \(5x^{2}=55\).
Step 2 ：Divide both sides of the equation by 5 to isolate \(x^{2}\). This gives us \(x^{2} = 11\).
Step 3 ：Apply the square root property, which states that if \(x^{2} = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\).
Step 4 ：Taking the square root of both sides gives us two solutions: \(x = \sqrt{11}\) and \(x = -\sqrt{11}\).
Step 5 ：Solving for \(x\) gives us approximately \(x = 3.3166247903554\) and \(x = -3.3166247903554\).
Step 6 ：Final Answer: The solution set is \(\boxed{\{3.3166247903554, -3.3166247903554\}}\).
