Step 1: Start with the equation 2x^2 + 8x + 6 = 0.
Step 2: Divide the entire equation by 2 to simplify it. This gives you x^2 + 4x + 3 = 0.
Step 3: Now, we need to factor the equation x^2 + 4x + 3.
Step 4: Look for two numbers that multiply to 3 (the constant term) and add up to 4 (the coefficient of x). The numbers 1 and 3 work because 1 * 3 = 3 and 1 + 3 = 4.
Step 5: Write the factored form of the equation as (x + 1)(x + 3) = 0.
Step 6: Set each factor equal to zero: x + 1 = 0 and x + 3 = 0.
Step 7: Solve for x in each equation. From x + 1 = 0, we get x = -1. From x + 3 = 0, we get x = -3.
Step 8: The solutions for x are -1 and -3.
Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring after simplifying.
Factoring – The solution involves recognizing how to factor a quadratic expression into binomials.
Zero Product Property – The solution applies the zero product property to find the values of x.
