Solve this quadratic equation. $$ -4 x=x^{2} $$

Question

UpStudy AI · Accepted Answer

Let's solve the quadratic equation step by step.

1. **Write the equation:**

$$
   -4x = x^2
   $$

2. **Bring all terms to one side:**

Add $$4x$$ to both sides to collect like terms:

$$
   -4x + 4x = x^2 + 4x \quad \Rightarrow \quad x^2 + 4x = 0
   $$

3. **Factor the quadratic:**

Factor out $$x$$ from the left-hand side:

$$
   x(x + 4) = 0
   $$

4. **Apply the Zero Product Property:**

Set each factor equal to zero:

- First factor: $$x = 0$$
   - Second factor: $$x + 4 = 0 \quad \Rightarrow \quad x = -4$$

5. **Write the solutions:**

The solutions to the equation are:

$$
   x = 0 \quad \text{or} \quad x = -4
   $$
The solutions are $$ x = 0 $$ and $$ x = -4 $$.

Solve this quadratic equation. \( -4 x=x^{2} \)