Question
Question 5 (1 point) Solve. \[ 2 x^{2}-39=33 \] a \( \pm 3 \) b no real number solution c \( \pm 6 \) d \( d \geq \sqrt{6} \)
Ask by Hilton Ingram. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x = \pm 6 \), so the correct answer is option (c).
Solution
Consider the equation
\[
2x^2 - 39 = 33.
\]
**Step 1.** Add \(39\) to both sides:
\[
2x^2 = 33 + 39 = 72.
\]
**Step 2.** Divide both sides by \(2\):
\[
x^2 = \frac{72}{2} = 36.
\]
**Step 3.** Take the square root of both sides:
\[
x = \pm \sqrt{36} = \pm 6.
\]
Thus, the solution is \( x = \pm 6 \), which corresponds to option (c).
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Extra Insights
To solve the equation \(2x^{2}-39=33\), start by simplifying it. Add 39 to both sides to get: \[2x^{2} = 72\]. Next, divide both sides by 2 to isolate \(x^{2}\): \[x^{2} = 36\]. Now take the square root of both sides, giving you \(x = \pm 6\). So the correct answer is \(c \pm 6\). As for common mistakes, many make the error of forgetting to isolate the squared variable before taking the square root. Ensure you've simplified correctly and double-check your steps to avoid miscalculations!