×2=81  solving quadratic Equations by factoring

It appears there might be a misunderstanding in the problem statement as presented. If you meant to solve \(x^2 = 81\) (which is a quadratic equation), here's how you solve it by factoring:

1. Rewrite the equation in standard quadratic form:
   \[
   x^2 - 81 = 0
   \]

2. Recognize that this is a difference of squares, which can be factored as:
   \[
   (x - 9)(x + 9) = 0
   \]

3. Set each factor equal to zero and solve for \(x\):
   \[
   x - 9 = 0 \quad \text{or} \quad x + 9 = 0
   \]

   \[
   x = 9 \quad \text{or} \quad x = -9
   \]

Thus, the solutions are \(x = 9\) and \(x = -9\).

Would you like any further details or have any questions about this solution?

Here are 8 related questions to expand your understanding:

1. How would you solve the equation \(x^2 - 25 = 0\) by factoring?
2. What are the solutions to the equation \(x^2 - 16 = 0\)?
3. How do you factor and solve \(x^2 - 49 = 0\)?
4. What are the roots of the equation \(x^2 - 64 = 0\)?
5. How would you solve \(x^2 - 4 = 0\) by factoring?
6. What are the solutions to the equation \(x^2 - 1 = 0\)?
7. How do you factor and solve \(x^2 - 100 = 0\)?
8. What are the roots of the equation \(x^2 - 121 = 0\)?

**Tip:** When dealing with quadratic equations, always look for patterns such as the difference of squares, perfect square trinomials, and common factors to simplify the factoring process.

Learn how to solve quadratic equations by factoring with a detailed step-by-step guide. Includes examples like x^2 = 81 and similar quadratic equations. Suitable for students in Grades 7-9.

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