Please help me solve this quadratic equation

$$x^2 + 2x+1=0 $$

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I am going to use the factoring method to solve this quadratic equation.

\[x^2+2x+1=0\]

The equation is already in the form $ax^2+bx+c=0$, so $a=1, b=2 , c=1$

1. List all factor pairs of $a*c$

- $1 \times 1$
- $-1\times -1$

2. Identify factors that add up to $b$

- Since $b=2$ then $1\times 1$ is the combination that adds up to $2$

3. Rewrite in factored form: \[(x+1)(x+1) =0\]

4. Since we know that if two number multiply each other and the product is $0$ then one of the two or both are zero (zero-product principle), then

\[x+1=0 \rightarrow x = -1\]

or

\[x+1=0 \rightarrow x = -1\]

therefore $x= -1 $ twice.

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