To solve the equation \( x(x - 3) + 2 = 0 \), follow these steps:

### Step 1: Expand the equation.
Distribute the \( x \) over \( (x - 3) \):

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

### Step 2: Factor the quadratic equation.
We are now looking to factor \( x^2 - 3x + 2 \). Find two numbers that multiply to \( 2 \) and add up to \( -3 \). These numbers are \( -1 \) and \( -2 \).

\[
x^2 - 3x + 2 = (x - 1)(x - 2) = 0
\]

### Step 3: 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 are \( x = 1 \) and \( x = 2 \).

Would you like further details on any step?

---

Here are 5 related questions to explore:

1. How do you factor a quadratic equation?
2. What is the general form of a quadratic equation?
3. Can quadratic equations have complex solutions?
4. How can you solve a quadratic equation using the quadratic formula?
5. What are the differences between factoring and completing the square?

**Tip**: Always check your solutions by plugging them back into the original equation.

Discover how to solve the quadratic equation x(x-3) + 2 = 0 using factoring techniques. This detailed, step-by-step guide helps students understand key algebraic concepts such as expanding, factoring, and solving quadratic equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation