Solve the equation.
-$$| 14 x | = 2 x ^ { 2 }$$
A) $\{ 0,7 , - 7 \}$
B) $\{ 0 , - 7 \}$
C) $\{ 0,7 \}$
D) No real solutions

Question

Quizplus · Accepted Answer

The equation $| 14x | = 2x^2$ can be solved by considering both positive and negative cases for the absolute value. For $14x = 2x^2$, rearranging gives $2x^2 - 14x = 0$, which simplifies to $x(2x - 14) = 0$, yielding solutions $x = 0$ and $x = 7$. For $-14x = 2x^2$, rearranging gives $2x^2 + 14x = 0$, which simplifies to $x(2x + 14) = 0$, yielding solutions $x = 0$ and $x = -7$. Combining these, the solution set is $\{0, 7, -7\}$.

Solve the Equation ∣14x∣=2x2| 14 x | = 2 x ^ { 2 }∣14x∣=2x2

Solve the Equation $| 14 x | = 2 x ^ { 2 }$