Solve the following equation. $$ 5 x^{2}=-x $$

Question

UpStudy AI · Accepted Answer

1. Rewrite the equation by moving all terms to one side:
   $$
   5x^2 + x = 0
   $$

2. Factor the left-hand side:
   $$
   x(5x + 1) = 0
   $$

3. Set each factor equal to zero and solve:

- For $$x = 0$$, the solution is:
     $$
     x = 0
     $$

- For $$5x + 1 = 0$$:
     $$
     5x = -1 \quad \Rightarrow \quad x = -\frac{1}{5}
     $$

Thus, the solutions to the equation are:
$$
x = 0 \quad \text{or} \quad x = -\frac{1}{5}
$$
The solutions are $$ x = 0 $$ and $$ x = -\frac{1}{5} $$.

Solve the following equation.