Solve x^2>-4x

$$x ^ { 2 } > - 4 x$$

Solve for x

$$x\in \left(-\infty,-4\right)\cup \left(0,\infty\right)$$

Solution Steps

Add 4x to both sides.

$$x^{2}+4x>0$$

Factor out x.

$$x\left(x+4\right)>0$$

For the product to be positive, x+4 and x have to be both negative or both positive. Consider the case when x+4 and x are both negative.

$$x+4<0 x<0$$

The solution satisfying both inequalities is x<-4.

$$x<-4$$

Consider the case when x+4 and x are both positive.

$$x>0 x+4>0$$

The solution satisfying both inequalities is x>0.

$$x>0$$

The final solution is the union of the obtained solutions.

$$x<-4\text{; }x>0$$