https://file.aiquickdraw.com/mathbot/file/1727336989899ekvyb584.jpg

The equation shown in the image is:

\[
343 + x^3 = 0
\]

Let's solve for \(x\).

### Step 1: Isolate \(x^3\)
Subtract 343 from both sides:

\[
x^3 = -343
\]

### Step 2: Solve for \(x\)
To find \(x\), take the cube root of both sides:

\[
x = \sqrt[3]{-343}
\]

Since \(343 = 7^3\), the cube root of \(-343\) is \(-7\):

\[
x = -7
\]

### Final Answer:
\[
x = -7
\]

Would you like further explanation or details? Here are some related questions you can explore:

1. What is the cube root of a negative number?
2. How do you solve higher-degree polynomial equations?
3. What are the properties of cube roots?
4. How does taking cube roots differ from square roots?
5. What happens when you raise negative numbers to odd powers?

**Tip:** The cube root of a negative number is always negative, unlike square roots which are undefined for negative numbers in the real number system.

Learn how to solve the cubic equation 343 + x^3 = 0. This problem involves finding the cube root of -343, with a detailed step-by-step solution suitable for Grades 9-10.

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