X²+3x+2=0

To solve the quadratic equation \(x^2 + 3x + 2 = 0\), we can factor the equation. 1. **Factoring**: We look for two numbers that multiply to \(2\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers \(1\) and \(2\) work because: - \(1 \times 2 = 2\) - \(1 + 2 = 3\) So we can factor the quadratic equation as: \[ (x + 1)(x + 2) = 0 \] 2. **Setting each factor to zero**: Now, we set each factor equal to zero: \[ x + 1 = 0 \quad \text{or} \quad x + 2 = 0 \] Solving these equations gives: \[ x = -1 \quad \text{or} \quad x = -2 \] 3. **Solutions**: The solutions to the equation \(x^2 + 3x + 2 = 0\) are: \[ x = -1 \quad \text{and} \quad x = -2 \] Thus, the final answer is \(x = -1\) and \(x = -2\).