Determine the most appropriate method and solve the following equation.
$x^2+6x+5=0$

• A. Factoring; $x=-1,x=-5$
• B. Quadratic Formula; $x=4.732,x=1.268$
• C. Factoring; $x=1,x=5$
• D. Quadratic Formula; $x=5,x=-1$

Answer: (A)

Verified step by step guidance

1. Step 1: Identify the quadratic equation given: \(x^2 + 6x + 5 = 0\).
2. Step 2: Look for a method to solve the quadratic. Since the equation is a quadratic trinomial, check if it can be factored easily by finding two numbers that multiply to 5 and add to 6.
3. Step 3: Find the factors of 5, which are 1 and 5, and see if their sum is 6. Since 1 + 5 = 6, the quadratic can be factored as \((x + 1)(x + 5) = 0\).
4. Step 4: Use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero: \(x + 1 = 0\) and \(x + 5 = 0\).
5. Step 5: Solve each simple equation for \(x\): \(x = -1\) and \(x = -5\). These are the solutions to the quadratic equation.