Solve the Quadratic Equation: x² - 3x + 2 = 0

Solve the following equation:

$x^2-3x+2=0$

To solve the quadratic equation $x^2 - 3x + 2 = 0$, we'll follow these steps:

• Step 1: Check for factorization. Assuming the quadratic can be factored, we look for two numbers that multiply to $c = 2$ and add to $b = -3$. These numbers are $-1$ and $-2$.
• Step 2: Factor the quadratic as $(x - 1)(x - 2) = 0$.
• Step 3: Solve each factor for $x$.

Now, let's solve the factors:
From $(x - 1) = 0$, we have $x = 1$.
From $(x - 2) = 0$, we have $x = 2$.

Thus, the solutions to the equation are $x_1 = 1$ and $x_2 = 2$.

Therefore, the solution to the problem is $x_1 = 1, x_2 = 2$.