x2-3x+2=0

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

1. Look for two numbers that multiply to \( 2 \) (the constant term) and add up to \( -3 \) (the coefficient of \( x \)).
2. The numbers \( -1 \) and \( -2 \) meet these criteria:
   • \( -1 \times -2 = 2 \)
   • \( -1 + (-2) = -3 \)

Thus, we can factor the equation as follows:

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

Now, set each factor equal to zero:

1. \( x - 1 = 0 \) ⟹ \( x = 1 \)
2. \( x - 2 = 0 \) ⟹ \( x = 2 \)

So the solutions to the equation \( x^2 - 3x + 2 = 0 \) are:

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