Question
\( 1 \leftarrow: \begin{array}{l}\text { Solve. } \\ 5 x^{2}-65=0\end{array} \)
Ask by Johnston Estrada. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( x = \sqrt{13} \) and \( x = -\sqrt{13} \).
Solution
We start with the equation:
5x² – 65 = 0
Step 1: Divide every term by 5 to simplify:
(5x²)/5 – 65/5 = 0/5
x² – 13 = 0
Step 2: Add 13 to both sides:
x² = 13
Step 3: Take the square root of both sides (remembering to consider both the positive and negative roots):
x = √13 or x = –√13
Thus, the solutions to the equation are:
x = √13 and x = –√13
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Simplify this solution The Deep Dive
To solve the equation \( 5x^2 - 65 = 0 \), you can start by isolating the \( x^2 \) term. Add 65 to both sides to get \( 5x^2 = 65 \). Then divide both sides by 5, giving you \( x^2 = 13 \). Finally, take the square root of both sides, which yields \( x = \pm \sqrt{13} \). Now you have two solutions: \( x = \sqrt{13} \) and \( x = -\sqrt{13} \). Happy calculating! For your next steps, remember that different forms of solutions display the results in various lights. Having both positive and negative solutions for quadratic equations is key, especially when interpreting real-world scenarios, like projectile trajectories. Don’t overlook this duality—it’s where the fun lies in math!
