https://file.aiquickdraw.com/mathbot/file/1726705561686qz4hvoi4.jpg

The equation displayed in the image is:

\[
u^2 - 500 = 0
\]

To solve this equation for \( u \), we can follow these steps:

### Step 1: Isolate \( u^2 \)
Add 500 to both sides of the equation:

\[
u^2 = 500
\]

### Step 2: Solve for \( u \)
Take the square root of both sides:

\[
u = \pm \sqrt{500}
\]

### Step 3: Simplify \( \sqrt{500} \)
\[
\sqrt{500} = \sqrt{100 \times 5} = 10\sqrt{5}
\]

Thus, the solution for \( u \) is:

\[
u = \pm 10\sqrt{5}
\]

This means there are two solutions:
\[
u = 10\sqrt{5} \quad \text{or} \quad u = -10\sqrt{5}
\]

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions you might explore:
1. How do we solve equations that have higher powers of \( u \), like \( u^3 - 500 = 0 \)?
2. What are the steps to solve a quadratic equation using the quadratic formula?
3. Can we solve this equation graphically? How would the graph look?
4. How do square roots of negative numbers work in the context of complex numbers?
5. How can we check the validity of the solution by substituting values back into the original equation?

**Tip:** Always remember that when you take the square root of a number in algebra, you need to consider both the positive and negative roots unless otherwise specified.

Learn how to solve the quadratic equation u^2 - 500 = 0 using square roots. This problem covers key algebraic concepts such as isolating the variable and simplifying square roots. Suitable for students in Grades 8-10.

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