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The equation provided is:

\[
3 = N g^2 - Q
\]

We are asked to solve for \( g \), assuming all variables are positive. To do this, we can follow these steps:

### Step 1: Isolate the \( g^2 \) term
First, add \( Q \) to both sides to move it to the left-hand side of the equation:

\[
3 + Q = N g^2
\]

### Step 2: Solve for \( g^2 \)
Next, divide both sides by \( N \) to solve for \( g^2 \):

\[
g^2 = \frac{3 + Q}{N}
\]

### Step 3: Solve for \( g \)
Finally, take the square root of both sides:

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

Since the problem specifies that all variables are positive and we do not use absolute values or the \( \pm \) sign, we take only the positive square root.

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

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

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Do you have any questions or would you like further details?

Here are 5 related questions for further practice:
1. If \( N = 4 \) and \( Q = 1 \), what is the value of \( g \)?
2. How does the value of \( g \) change as \( N \) increases?
3. What happens to the value of \( g \) if \( Q = 0 \)?
4. Can you rewrite the equation in terms of \( Q \) instead of \( g \)?
5. What is the general form of a quadratic equation like this one, and how does it compare?

**Tip**: When solving equations involving squares, always be mindful of the conditions set by the problem regarding positive or negative roots.

Solve the following equation for g: 3 = N g^2 - Q

Learn how to solve the equation 3 = N g^2 - Q for g, using algebraic methods. This step-by-step solution covers key quadratic concepts and is suitable for students in Grades 10-12. The solution assumes all variables are positive.

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