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Solve $\color{blue}{x^2+x = 0}$ using factoring.

## Answer

$$ \color{blue}{ x_1 = -1 }~~ \text{and}~~ \color{blue}{ x_2 = 0 } $$

## Explanation

First we need to factor trinomial $ \color{blue}{ x^2+x } $ and than we use factored form to solve an equation $ \color{blue}{ x^2+x = 0} $.

** Step 1:** Factor $ x $ out of $ x^{2}+x $ :

$$ x^{2}+x = x \cdot( x+1 ) $$

** Step 2:** Set each factor to zero and solve equations.

$$ \begin{array}{ccc}
\begin{aligned}
x &= 0 \\
~ & ~
\end{aligned} & ~ & \begin{aligned}
x+1 &= 0 \\
x &= -1
\end{aligned}
\end{array} $$

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