x²+6x+8=0. solve this by factoring. show your work
To solve the quadratic equation x² + 6x + 8 = 0 by factoring, we first need to find two numbers that multiply to 8 (the constant term) and add up to 6 (the coefficient of the x term).
The two numbers that work in this case are 2 and 4. So, we can rewrite the equation as:
x² + 2x + 4x + 8 = 0
Now, we can factor by grouping:
x(x + 2) + 4(x + 2) = 0
(x + 2)(x + 4) = 0
Now, set each factor to zero and solve for x:
x + 2 = 0
x = -2
x + 4 = 0
x = -4
Therefore, the solutions to the equation x² + 6x + 8 = 0 are x = -2 and x = -4.