https://file.aiquickdraw.com/mathbot/file/1726809096286o5sbdp5s.jpg

The equation given in the image is:

\[
2x^2 = 200
\]

Let's solve this step by step:

1. **Divide both sides by 2** to isolate \( x^2 \):
\[
x^2 = \frac{200}{2} = 100
\]

2. **Take the square root** of both sides:
\[
x = \pm \sqrt{100}
\]

3. Since \( \sqrt{100} = 10 \), the solution is:
\[
x = \pm 10
\]

Thus, the two possible solutions are \( x = 10 \) and \( x = -10 \).

Would you like more details on any of the steps?

Here are 5 related questions to explore further:
1. How would you solve the equation if it were \( 2x^2 = 50 \)?
2. What happens if \( x^2 = -100 \)?
3. How do you solve cubic equations like \( 2x^3 = 200 \)?
4. What is the general solution for \( ax^2 + bx + c = 0 \)?
5. How do square roots of negative numbers work with complex numbers?

**Tip**: Always check your solution by substituting it back into the original equation!

Step-by-step guide to solving the quadratic equation 2x^2 = 200. This problem covers key algebraic concepts such as isolating x^2 and using square roots to find the solutions. Suitable for Grades 7-9 students.

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