Solve the equation.
-$$| x | = x ^ { 2 } + 7 x$$
A) $0 , - 8$
B) $0 , - 6$
C) $- 8 , - 6$
D) $0 , - 8 , - 6$

Question

Quizplus · Accepted Answer

The equation $| x | = x ^ { 2 } + 7 x$ can be solved by considering two cases: $x \geq 0$ and $x < 0$. For $x \geq 0$, $| x | = x$, so the equation becomes $x = x^2 + 7x$, which simplifies to $x^2 + 6x = 0$, factoring out $x$ gives $x(x + 6) = 0$, leading to solutions $x = 0$ and $x = -6$. However, $x = -6$ does not satisfy $x \geq 0$, so we discard it. For $x < 0$, $| x | = -x$, so the equation becomes $-x = x^2 + 7x$, which simplifies to $x^2 + 8x = 0$, factoring gives $x(x + 8) = 0$, leading to solutions $x = 0$ and $x = -8$. Since $x = 0$ is already considered and $x = -8$ satisfies $x < 0$, the final solutions are $x = 0$ and $x = -8$.

Solve the Equation ∣x∣=x2+7x| x | = x ^ { 2 } + 7 x∣x∣=x2+7x

Solve the Equation $| x | = x ^ { 2 } + 7 x$