Question

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
o solution.\

Explanation:

Step1: Take square root of both sides

To solve the equation \(x^2 = 54\) for \(x\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution. So we have \(x=\pm\sqrt{54}\).

Step2: Simplify the square root

We simplify \(\sqrt{54}\) by factoring 54 into its prime factors. \(54 = 9\times6\), and since \(\sqrt{9}=3\), we can rewrite \(\sqrt{54}\) as \(\sqrt{9\times6}=3\sqrt{6}\). So the solutions for \(x\) are \(x = 3\sqrt{6}, - 3\sqrt{6}\).

Answer:

\(3\sqrt{6}, -3\sqrt{6}\)