This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the quadratic equation \( x^2 + 5x + 6 = 0 \) step by step, follow these steps: 1. Identify the coefficients: \( a = 1 \) (coefficient of \( x^2 \)) \( b = 5 \) (coefficient of \( x \)) \( c = 6 \) (constant term) 2. Factor the quadratic: We need two numbers that multiply to \( c \) (6) and add to \( b \) (5). The numbers 2 and 3 work because \( 2 × 3 = 6 \) and \( 2 + 3 = 5 \). Thus, we can factor the equation as \( (x + 2)(x + 3) = 0 \). 3. Set each factor to zero: \( x + 2 = 0 \) or \( x + 3 = 0 \) 4. Solve for \( x \): From \( x + 2 = 0 \): \[ x = -2 \] From \( x + 3 = 0 \): \[ x = -3 \] 5. Final solutions: The solutions to the equation \( x^2 + 5x + 6 = 0 \) are \( x = -2 \) and \( x = -3 \).