Final answer:
To solve the equation 2x³+10x²+12x=0, factor out an x, set each factor equal to zero, and solve. Use the quadratic formula to solve the resulting quadratic equation. The solutions are x = -3 and x = -1.
Step-by-step explanation:
To solve the equation 2x³+10x²+12x=0, we can factor out an x from each term to get x(2x²+10x+12)=0. Then, we can set each factor equal to zero and solve:
- x = 0
- 2x²+10x+12 = 0
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. Factoring does not work in this case, so let's use the quadratic formula:
x = (-b ± √(b²-4ac))/(2a)
For the equation 2x²+10x+12=0, a = 2, b = 10, and c = 12. Plugging these values into the quadratic formula, we get:
x = (-10 ± √(10²-4(2)(12)))/(2(2))
Simplifying further, we have:
x = (-10 ± √(100-96))/(4)
x = (-10 ± √4)/(4)
x = (-10 ± 2)/(4)
So, the solutions are: