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The question visible in your image asks you to solve for \( x \) using the square root property:

\[
6x^2 - 62 = -20
\]

### Solution:
1. Start by isolating the term with \( x^2 \).
   \[
   6x^2 - 62 = -20
   \]
   Add 62 to both sides:
   \[
   6x^2 = 42
   \]

2. Divide both sides by 6:
   \[
   x^2 = \frac{42}{6}
   \]
   Simplifying:
   \[
   x^2 = 7
   \]

3. Now, apply the square root property. Taking the square root of both sides:
   \[
   x = \pm \sqrt{7}
   \]

Thus, the two possible solutions for \( x \) are:
\[
x = \sqrt{7} \quad \text{or} \quad x = -\sqrt{7}
\]

### Final Answer:
Enter the answers as a list: `sqrt(7), -sqrt(7)`.

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Would you like more details or have any questions on this?

Here are some related questions to further explore this topic:
1. How do you handle equations where the quadratic term has a coefficient larger than 1?
2. What if the equation had no real solutions, how would you determine that?
3. How can you verify the solutions after finding them?
4. What are other methods of solving quadratic equations besides using the square root property?
5. How does completing the square compare to solving by taking square roots?

**Tip:** Always check if you can simplify the square root when solving quadratic equations.

Solve for x using the square root property: 6x^2 - 62 = -20

Learn how to solve the quadratic equation 6x^2 - 62 = -20 using the square root property. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 9-11.

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