Solve x^2+5x

$$x ^ { 2 } + 5 x$$

Factor

$$x\left(x+5\right)$$

Solution Steps

Factor out x.

$$x\left(x+5\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$x^{2}+5x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-5±\sqrt{5^{2}}}{2}$$

Take the square root of 5^{2}.

$$x=\frac{-5±5}{2}$$

Now solve the equation x=\frac{-5±5}{2} when ± is plus. Add -5 to 5.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-5±5}{2} when ± is minus. Subtract 5 from -5.

$$x=-\frac{10}{2}$$

Divide -10 by 2.

$$x=-5$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -5 for x_{2}.

$$x^{2}+5x=x\left(x-\left(-5\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$x^{2}+5x=x\left(x+5\right)$$

Evaluate

$$x\left(x+5\right)$$