X^2+6x+9=0 factor the left hand side of the equation into two linear factors

To factor the quadratic equation \( x^2 + 6x + 9 = 0 \), follow these steps:

1. **Identify the quadratic expression**: \( x^2 + 6x + 9 \).
2. **Factor the quadratic expression**:
   - Notice that the expression can be written as a perfect square trinomial.
   - \( x^2 + 6x + 9 \) can be factored as \( (x + 3)(x + 3) \) or \( (x + 3)^2 \).

So, the factored form of the equation is:

\[
(x + 3)(x + 3) = 0
\]

or equivalently:

\[
(x + 3)^2 = 0
\]

Would you like more details or have any other questions? Here are some related questions to consider:

1. What is the next step to solve \( (x + 3)^2 = 0 \)?
2. How do you determine whether a quadratic expression is a perfect square trinomial?
3. Can all quadratic equations be factored similarly?
4. How can the solutions to \( (x + 3)(x + 3) = 0 \) be interpreted?
5. What methods can be used to factor non-perfect square trinomials?

**Tip**: Always check if a quadratic expression can be factored as a perfect square trinomial, which simplifies the process significantly.

Learn how to factor the quadratic equation x^2 + 6x + 9 by recognizing it as a perfect square trinomial. This tutorial provides a step-by-step solution, including key algebraic concepts like factoring and perfect squares. Suitable for students in Grades 8-10.

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