Question
1.2 Homework Solve the following equation by the square root method. \( x^{2}=144 \) Select the correct choice below and fill in any answer boxes within your choice. A. The solution set is \( \{\square \). \( 50 \%, 60 \) (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) 1.2 .31 . B. There are no solutions.
Ask by Smith Edwards. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution set is \( \{-12, 12\} \).
Solution
To solve the equation \( x^{2} = 144 \) using the square root method, follow these steps:
1. **Take the square root of both sides:**
\[
\sqrt{x^{2}} = \sqrt{144}
\]
2. **Simplify both sides:**
\[
|x| = 12
\]
3. **Solve for \( x \):**
\[
x = 12 \quad \text{or} \quad x = -12
\]
**Solution Set:**
\[
\{ -12, 12 \}
\]
**Therefore, the correct choice is:**
**A. The solution set is \( \{ -12, 12 \} \).**
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Simplify this solution The Deep Dive
To solve the equation \( x^{2} = 144 \) using the square root method, we take the square root of both sides. This gives us \( x = \pm \sqrt{144} \), which simplifies to \( x = \pm 12 \). Therefore, the solution set is \( \{ -12, 12 \} \). The solution set \( \{ -12, 12 \} \) showcases that every positive number has a corresponding negative counterpart when squared, revealing the beauty of symmetry in mathematics. It’s important to remember that squaring a number always yields a positive result or zero, which is why we need the positive and negative roots in the solution.
