Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
Quadratic equation:
x^2 + 5x + 6 = 0
To solve, we need to factor the quadratic equation. We need to find two numbers that multiply to 6 and add up to 5. The two numbers are 2 and 3.
Therefore, the factored form of the equation is:
(x + 2)(x + 3) = 0
Setting each factor to zero gives:
x + 2 = 0 or x + 3 = 0
x = -2 or x = -3
Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are -2 and -3.