Question
a. \( \quad 2 x^{2}-18=0 \)
Ask by Vaughan Bates. in Mongolia
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 3 \) or \( x = -3 \)
Solution
1. Start with the equation:
\[
2x^2 - 18 = 0
\]
2. Add 18 to both sides:
\[
2x^2 = 18
\]
3. Divide both sides by 2:
\[
x^2 = 9
\]
4. Take the square root of both sides (remembering to include both positive and negative roots):
\[
x = \pm 3
\]
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Simplify this solution The Deep Dive
To solve the equation \( 2x^2 - 18 = 0 \), you can first isolate the \( x^2 \) term. Start by adding 18 to both sides to get \( 2x^2 = 18 \). Then, divide both sides by 2, yielding \( x^2 = 9 \). Finally, take the square root of both sides to find \( x = 3 \) or \( x = -3 \). Now you have two solutions: \( x = 3 \) and \( x = -3 \). Quadratics like this one are fun because they often represent simple parabolas, and each solution represents the points where the parabola intersects the x-axis!
