Answer:
-4
Explanation:
For e^(-2x) = 0, there is no value of x that can make this true. Exponential functions with a base greater than 1 never equal zero. Therefore, this factor does not provide a solution.
- For 4x + x² = 0, we can rewrite the equation as x(4 + x) = 0.
3. Now, we have two factors: x = 0 and 4 + x = 0. Let's solve each factor separately:
- For x = 0, this provides one solution: x = 0.
- For 4 + x = 0, we subtract 4 from both sides: x = -4. This gives us another solution: x = -4.
4. Therefore, the solutions to the equation 4xe^(-2x) + x²e^(-2x) = 0 are x = 0 and x = -4.
Notice that both terms in the equation have a common factor of e^(-2x). We can factor it out: e^(-2x)(4x + x²) = 0.
2. Now, we have two factors: e^(-2x) = 0 and 4x + x² = 0. Let's solve each factor separately: