https://file.aiquickdraw.com/mathbot/file/1725823731115umovadjs.jpg

The equation provided in the image is:

\[
S = Ng^3 - Q
\]

We are tasked with solving for \( g \).

### Step-by-step solution:
1. Start with the equation:
   \[
   S = Ng^3 - Q
   \]

2. Add \( Q \) to both sides to isolate the \( Ng^3 \) term:
   \[
   S + Q = Ng^3
   \]

3. Divide both sides by \( N \) to further isolate \( g^3 \):
   \[
   \frac{S + Q}{N} = g^3
   \]

4. Take the cube root of both sides to solve for \( g \):
   \[
   g = \sqrt[3]{\frac{S + Q}{N}}
   \]

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

\[
g = \sqrt[3]{\frac{S + Q}{N}}
\]

### Do you need any further details on the solution or have any questions?

Here are 5 related questions to further explore this topic:
1. How would you solve for \( g \) if the equation involved a higher power of \( g \)?
2. What happens to the solution if \( N = 0 \)?
3. How can you check if your solution is correct by substituting \( g \) back into the original equation?
4. What would change if the equation was \( S = Ng^4 - Q \)?
5. Can the cube root of a negative number be real in this context?

**Tip:** When solving for variables raised to powers, isolating the term with the variable first is a key step before applying any roots.

Solve the following equation for g: S = Ng^3 - Q

Learn how to solve the cubic equation S = Ng^3 - Q for g. This problem covers key algebraic concepts and techniques such as isolating variables and using cube roots. Suitable for high school students in Grades 9-12.

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