Question
Solve \( x^{2}=18 \), 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." \( x=\square \)
Ask by Edwards Erickson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 3\sqrt{2},\ -3\sqrt{2} \)
Solution
\( x^2 = 18 \)
1. Take the square root of both sides:
\[
x = \pm \sqrt{18}
\]
2. Simplify \(\sqrt{18}\) by recognizing that \(18 = 9 \times 2\):
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]
Thus, the solutions are:
\[
x = 3\sqrt{2},\quad x = -3\sqrt{2}
\]
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Simplify this solution Bonus Knowledge
To solve the equation \( x^{2} = 18 \), we start by taking the square root of both sides. This gives us: \[ x = \pm \sqrt{18}. \] Next, we can simplify \( \sqrt{18} \). It can be expressed as \( \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \). Therefore, the solutions are: \[ x = 3\sqrt{2}, -3\sqrt{2}. \] So the final answer is: \( x = 3\sqrt{2}, -3\sqrt{2} \)
