Question
\( 2 x^{2}+4=14 \) The solve the equation by the square root property. (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
Ask by Weston Ross. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -\sqrt{5},\ \sqrt{5} \)
Solution
To solve the equation \( 2x^{2} + 4 = 14 \) using the square root property, follow these steps:
1. **Isolate the squared term:**
\[
2x^{2} + 4 = 14 \\
2x^{2} = 14 - 4 \\
2x^{2} = 10 \\
x^{2} = \frac{10}{2} \\
x^{2} = 5
\]
2. **Apply the square root property:**
\[
x = \pm \sqrt{5}
\]
**Final Answer:**
\[
-\sqrt{5},\ \sqrt{5}
\]
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Explain 
Simplify this solution Beyond the Answer
First, let's isolate the quadratic term by subtracting 4 from both sides: \( 2x^{2} = 10 \). Next, we can divide both sides by 2 to simplify: \( x^{2} = 5 \). Now, applying the square root property, we take the square root of both sides: \( x = \pm \sqrt{5} \). Thus, the solutions are: \( x = \sqrt{5}, -\sqrt{5} \).
