Solve the quadratics by square root method.  9n^2-6=30

To solve the quadratic equation \( 9n^2 - 6 = 30 \) using the square root method, follow these steps:

### Step 1: Isolate the quadratic term
First, move all constants to the right-hand side of the equation:
\[
9n^2 = 30 + 6
\]
\[
9n^2 = 36
\]

### Step 2: Divide by the coefficient of \(n^2\)
Divide both sides of the equation by 9 to simplify:
\[
n^2 = \frac{36}{9}
\]
\[
n^2 = 4
\]

### Step 3: Take the square root of both sides
Now, take the square root of both sides to solve for \(n\):
\[
n = \pm \sqrt{4}
\]
\[
n = \pm 2
\]

### Final Answer:
The solutions are:
\[
n = 2 \quad \text{or} \quad n = -2
\]

Would you like more details on any of the steps?

Here are 5 related questions you might find helpful:
1. How do you solve quadratics when they are not in standard form?
2. What is the square root method, and how does it differ from factoring?
3. Can the square root method be used for all types of quadratic equations?
4. How do you solve quadratics that result in complex solutions?
5. What are other methods for solving quadratic equations?

**Tip:** Always simplify the equation as much as possible before taking the square root.

Solve the quadratics by square root method. 9n^2 - 6 = 30

Learn how to solve the quadratic equation 9n^2 - 6 = 30 step-by-step using the square root method. This solution covers key algebraic concepts such as isolating the quadratic term, simplifying, and solving using square roots. Suitable for students in Grades 7-9.

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