can u solve 2(x+3)^2-6=0 by rewriting in form of ax^2 + bx + c = 0

Let's solve the equation \(2(x + 3)^2 - 6 = 0\) by rewriting it in the standard quadratic form \(ax^2 + bx + c = 0\).

### Step 1: Start with the given equation
\[
2(x + 3)^2 - 6 = 0
\]

### Step 2: Add 6 to both sides to isolate the squared term
\[
2(x + 3)^2 = 6
\]

### Step 3: Divide both sides by 2 to simplify
\[
(x + 3)^2 = 3
\]

### Step 4: Expand the squared term
\[
(x + 3)(x + 3) = x^2 + 6x + 9
\]
So, the equation becomes:
\[
x^2 + 6x + 9 = 3
\]

### Step 5: Subtract 3 from both sides to get the equation in standard form
\[
x^2 + 6x + 6 = 0
\]

### Final Answer
The equation \(2(x + 3)^2 - 6 = 0\) rewritten in the standard form is:
\[
x^2 + 6x + 6 = 0
\]

Would you like any further clarification on this problem? Here are some related questions for practice:

1. How would the solution change if the constant on the right side were different?
2. Can you solve the quadratic equation \(x^2 + 6x + 6 = 0\) using the quadratic formula?
3. What is the vertex of the parabola represented by the equation \(x^2 + 6x + 6 = 0\)?
4. How does the graph of \(x^2 + 6x + 6 = 0\) compare to the graph of \(x^2 = 0\)?
5. What are the roots of \(x^2 + 6x + 6 = 0\) and what do they signify geometrically?

**Tip:** Always double-check your expanded forms when working with squared terms to avoid any errors in simplification.

Learn how to rewrite the equation 2(x+3)^2 - 6 = 0 into the standard quadratic form ax^2 + bx + c = 0. This detailed step-by-step solution covers algebraic manipulation and the derivation of the quadratic formula. Suitable for high school students studying algebra.

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