Solve the equation below algebraically.
$- x ^ { 2 } e ^ { 2 x } - 7 x e ^ { 2 x } = 0$
A) $- 7$ and $- 6$
B) $- 6$ and $6$
C) $- 7$ and $6$
D) $0$ and $6$
E) $- 7$ and $0$

Question

Quizplus · Accepted Answer

First, factor out the common term $xe^{2x}$ from the given equation: $xe^{2x}(-x - 7) = 0$. This gives us two solutions: $x = 0$ from the $xe^{2x}$ term (since $xe^{2x} = 0$ implies $x = 0$) and $x = -7$ from solving $-x - 7 = 0$, which simplifies to $x = -7$.

Solve the Equation Below Algebraically −x2e2x−7xe2x=0- x ^ { 2 } e ^ { 2 x } - 7 x e ^ { 2 x } = 0−x2e2x−7xe2x=0

Solve the Equation Below Algebraically $- x ^ { 2 } e ^ { 2 x } - 7 x e ^ { 2 x } = 0$