Solve Using the Quadratic Formula x(x+1)=0

$x (x + 1) = 0$

Step 1

Simplify the left side.

Simplify $x (x + 1)$ .

Apply the distributive property.

$x \cdot x + x \cdot 1 = 0$

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 = 0$

Multiply $x$ by $1$ .

$x^{2} + x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 1$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 0$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 0}}{2 \cdot 1}$

Multiply $- 4$ by $0$ .

$x = \frac{- 1 \pm \sqrt{1 + 0}}{2 \cdot 1}$

Add $1$ and $0$ .

$x = \frac{- 1 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$x = \frac{- 1 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 1 \pm 1}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 0, - 1$