Question
Solve for \( x \) using the square root property. \( x^{2}-29=0 \) \( x=1 \)
Ask by Deleon Frazier. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( x = \sqrt{29} \) and \( x = -\sqrt{29} \).
Solution
We start with the equation
\[
x^{2} - 29 = 0.
\]
**Step 1: Isolate the squared term.**
Add \(29\) to both sides:
\[
x^{2} = 29.
\]
**Step 2: Apply the square root property.**
Taking the square root of both sides, remember to include both positive and negative solutions:
\[
x = \pm \sqrt{29}.
\]
Thus, the solutions are
\[
x = \sqrt{29} \quad \text{or} \quad x = -\sqrt{29}.
\]
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Simplify this solution Beyond the Answer
To solve the equation \( x^{2} - 29 = 0 \), we first isolate \( x^{2} \) by adding 29 to both sides, giving us \( x^{2} = 29 \). Next, we apply the square root property, which tells us that \( x \) can be either the positive or negative square root of 29. Thus, we have \( x = \sqrt{29} \) or \( x = -\sqrt{29} \). Therefore, the solutions are \( x \approx 5.39 \) and \( x \approx -5.39 \). Now, it's important to double-check mistakes. If you initially thought that \( x = 1 \) was a solution, remember that squaring 1 yields 1, which won’t satisfy the original equation since \( 1 - 29 = -28 \) is not equal to 0. Always check your work to avoid such slip-ups!
