Question
1 Solve the equation \( 2 x^{2}+1=19 \) for \( x \)
Ask by Greene Fowler. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 3 \) or \( x = -3 \)
Solution
To solve the equation \( 2x^{2} + 1 = 19 \) for \( x \), follow these steps:
1. **Subtract 1 from both sides:**
\[
2x^{2} + 1 - 1 = 19 - 1
\]
\[
2x^{2} = 18
\]
2. **Divide both sides by 2:**
\[
\frac{2x^{2}}{2} = \frac{18}{2}
\]
\[
x^{2} = 9
\]
3. **Take the square root of both sides:**
\[
x = \pm \sqrt{9}
\]
\[
x = \pm 3
\]
**Solutions:**
\[
x = 3 \quad \text{or} \quad x = -3
\]
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Simplify this solution Mind Expander
To solve the equation \( 2x^{2} + 1 = 19 \), start by isolating the \( x^{2} \) term. Subtract 1 from both sides to get \( 2x^{2} = 18 \). Then, divide both sides by 2 to find \( x^{2} = 9 \). Finally, take the square root of both sides to get \( x = 3 \) or \( x = -3 \). So the solutions are \( x = 3 \) and \( x = -3 \). If you substitute these values back into the original equation, you'll see that both \( 3 \) and \( -3 \) satisfy it, confirming your solutions are indeed correct!
