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 $a + b i$ .)

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Answer

Final Answer: The solution set is ${3.3166247903554, - 3.3166247903554}$ .

Steps

Step 1 ：Given the equation $5 x^{2} = 55$ .

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 ${3.3166247903554, - 3.3166247903554}$ .