https://file.aiquickdraw.com/mathbot/file/1727264058987riqkh0lp.jpg

The image you uploaded shows a quadratic equation in the form:

\[
x(x - 3) = -2
\]

Let's solve this step by step:

### Step 1: Expand the left side
First, expand the expression on the left side of the equation:

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

So, the equation becomes:

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

### Step 2: Move all terms to one side
Next, add 2 to both sides to set the equation equal to 0:

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

### Step 3: Solve using factoring
Now, we factor the quadratic equation. We need two numbers that multiply to 2 and add up to -3. These numbers are -1 and -2:

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

### Step 4: Solve for x
Set each factor equal to 0:

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

Thus, the solutions are:

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

### Final Answer:
The solutions to the equation \( x(x - 3) = -2 \) are \( x = 1 \) and \( x = 2 \).

Would you like further details or have any questions?

Here are five related questions you can explore:
1. How can we verify the solutions by substituting them back into the original equation?
2. What are other methods to solve quadratic equations, like completing the square or using the quadratic formula?
3. What if the equation was \( x(x - 3) = 2 \)? How would the solutions change?
4. Can all quadratic equations be factored easily? Why or why not?
5. How does the discriminant help us determine the nature of the roots of a quadratic equation?

**Tip:** When factoring quadratic equations, always look for two numbers that multiply to the constant term and add up to the coefficient of the linear term.

Solve the quadratic equation: x(x - 3) = -2.

Learn how to solve the quadratic equation x(x - 3) = -2 using expansion, factoring, and the zero product property. This step-by-step solution is suitable for students in Grades 8-10 studying algebra and quadratic equations.

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