https://file.aiquickdraw.com/mathbot/file/172572738742235vjt049.jpg

The image shows part of a quadratic equation:

\[
x^2 - 3x - 2 = 0
\]

This is a standard quadratic equation. To solve it, we can use factoring, completing the square, or the quadratic formula. Factoring is the simplest method if the equation is factorable.

Let's factor this equation by finding two numbers that multiply to give the constant term (-2) and add to give the coefficient of the middle term (-3).

We are looking for two numbers whose product is \(-2\) and sum is \(-3\). These numbers are \(-2\) and \(-1\).

So, we can factor the quadratic equation as:

\[
(x - 2)(x + 1) = 0
\]

Setting each factor equal to zero:

\[
x - 2 = 0 \quad \text{or} \quad x + 1 = 0
\]

Solving for \(x\):

\[
x = 2 \quad \text{or} \quad x = -1
\]

Thus, the solutions are \(x = 2\) and \(x = -1\).

Would you like any more details or further clarifications?

Here are five related questions to deepen your understanding:
1. How would you solve this quadratic using the quadratic formula?
2. What are the conditions for a quadratic equation to be factorable?
3. How can you use completing the square to solve this equation?
4. Can you graph the equation \(x^2 - 3x - 2 = 0\) and explain its roots geometrically?
5. How do the solutions \(x = 2\) and \(x = -1\) relate to the parabola's intersection with the x-axis?

**Tip:** When factoring, always check if the equation can be simplified by finding two numbers that satisfy both multiplication and addition conditions. If it’s not easily factorable, try the quadratic formula.

Solve the quadratic equation x^2 - 3x - 2 = 0 by factoring.

Learn how to solve the quadratic equation x^2 - 3x - 2 using factoring. This problem covers key algebraic concepts such as factoring, solving quadratic equations, and applying the Zero-Product Property. Suitable for students in Grades 8-10.

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