To solve the quadratic equation \( x^2 - 3x + 2 = 0 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 1 \), \( b = -3 \), and \( c = 2 \). Substituting these values into the formula gives:

\[
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(2)}}{2(1)}
\]

\[
x = \frac{3 \pm \sqrt{9 - 8}}{2}
\]

\[
x = \frac{3 \pm \sqrt{1}}{2}
\]

\[
x = \frac{3 \pm 1}{2}
\]

So, the solutions are:

\[
x = \frac{4}{2} = 2 \quad \text{and} \quad x = \frac{2}{2} = 1
\]

The solutions to the equation are \( x = 2 \) and \( x = 1 \).

Would you like a detailed explanation of the steps or have any other questions?

### Related Questions

1. How do you derive the quadratic formula?
2. What is the discriminant, and how does it determine the nature of the roots?
3. Can quadratic equations have complex roots? If so, how are they found?
4. How can we complete the square to solve a quadratic equation?
5. What are the graphical interpretations of the solutions to a quadratic equation?
6. How does the value of the coefficient \( a \) affect the shape of the parabola?
7. Can the quadratic formula be used for non-quadratic equations?
8. What are some real-life applications of quadratic equations?

**Tip:** Always check the discriminant (\( b^2 - 4ac \)) first to determine the number and type of solutions for a quadratic equation.

Learn how to solve the quadratic equation x^2 - 3x + 2 = 0 with a detailed step-by-step solution using the quadratic formula. This problem covers key algebraic concepts and the quadratic formula. Suitable for students in Grades 9-12.

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