Solve the following quadratic equation for all values of xx in simplest form.
3, left parenthesis, x, squared, minus, 6, right parenthesis, minus, 2, equals, 1
3(x 
2
 −6)−2=
1

We are given the quadratic equation:

\[
3(x^2 - 6) - 2 = 1
\]

Let's solve this step by step:

### Step 1: Expand the expression
First, distribute the \(3\) across the terms inside the parentheses:

\[
3(x^2 - 6) = 3x^2 - 18
\]

So the equation becomes:

\[
3x^2 - 18 - 2 = 1
\]

### Step 2: Combine like terms
Combine \(-18\) and \(-2\) on the left side:

\[
3x^2 - 20 = 1
\]

### Step 3: Isolate the quadratic term
Add 20 to both sides to move the constant term to the right:

\[
3x^2 = 21
\]

### Step 4: Solve for \(x^2\)
Divide both sides by 3 to isolate \(x^2\):

\[
x^2 = 7
\]

### Step 5: Solve for \(x\)
Take the square root of both sides:

\[
x = \pm \sqrt{7}
\]

Thus, the solutions to the equation are:

\[
x = \sqrt{7} \quad \text{or} \quad x = -\sqrt{7}
\]

### Final Answer:
The solutions are:

\[
x = \pm \sqrt{7}
\]

---

Would you like more details or have any questions about this? Here are some related questions:

1. How do you solve quadratic equations using the quadratic formula?
2. What are the methods to factor quadratic equations?
3. Can all quadratic equations be solved by factoring?
4. How do you graph a quadratic equation?
5. What is the significance of the discriminant in quadratic equations?

**Tip:** Always check if you can simplify an equation by factoring before using the quadratic formula. It often makes the problem easier to solve!

Solve the following quadratic equation for all values of x in simplest form: 3(x^2 - 6) - 2 = 1

Learn how to solve the quadratic equation 3(x^2 - 6) - 2 = 1 in simplest form. This detailed solution involves expanding the expression, combining like terms, isolating the quadratic term, and solving by square roots. Suitable for Grades 8-10, covering key concepts in algebra and quadratic equations.

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