Solve the quadratic equatun using fuve metuod \( x^{2}+8 x+12=0 \)

To solve the quadratic equation \( x^{2} + 8x + 12 = 0 \) using factoring, we can look for two numbers that multiply to 12 and add to 8. Those numbers are 2 and 6! So, we can rewrite the equation as \( (x + 2)(x + 6) = 0 \). Setting each factor to zero gives us \( x + 2 = 0 \) or \( x + 6 = 0 \). Thus, the solutions are \( x = -2 \) and \( x = -6 \). Another method involves using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). For this equation, \( a = 1 \), \( b = 8 \), and \( c = 12 \). Plugging in these values, we get \( x = \frac{-8 \pm \sqrt{8^2 - 4(1)(12)}}{2(1)} \). The discriminant is 16, leading to \( x = \frac{-8 \pm 4}{2} \). So, we ultimately get \( x = -2 \) and \( x = -6 \), consistent with our earlier solution!