Question

Please help me solve this  quadratic equation

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

 

Comments

Yes, please! I'm interested in learning more about how math can be used to analyze data in practical situations.

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Yes, please! I'm interested in learning more about how math can be used to analyze data in practical situations.

Answer 1

Mathematical concepts such as statistical analysis, probability, and graphing can be used to analyze data in everyday life. For example, you can use statistics to interpret survey results or use graphs to visualize trends. Would you like more specific examples?

Answer 2

Mathematical concepts such as statistical analysis, probability, and graphing can be used to analyze data in everyday life. For example, you can use statistics to interpret survey results or use graphs to visualize trends. Would you like more specific examples?

Answer 3

 

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.

 

Answer 4

Use the quadratic formula
\[
x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}
\]
Once in standard form, identify \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) from the original equation and plug them into the quadratic formula.
\[
\begin{aligned}
&x^2+2 x+1=0 \\
&a=1 \\
&b=2 \\
&c=1 \\
&x=\frac{-2 \pm \sqrt{2^2-4 \cdot 1 \cdot 1}}{2 \cdot 1}
\end{aligned}
\]

Evaluate the exponent
\[
\begin{aligned}
&x=\frac{-2 \pm \sqrt{2^2-4 \cdot 1 \cdot 1}}{2 \cdot 1} \\
&x=\frac{-2 \pm \sqrt{4-4 \cdot 1 \cdot 1}}{2 \cdot 1}
\end{aligned}
\]

Multiply the numbers
\[
\begin{aligned}
&x=\frac{-2 \pm \sqrt{4-4 \cdot 1 \cdot 1}}{2 \cdot 1} \\
&x=\frac{-2 \pm \sqrt{4-4}}{2 \cdot 1}
\end{aligned}
\]

Subtract the numbers
\[
\begin{aligned}
&x=\frac{-2 \pm \sqrt{4-4}}{2 \cdot 1} \\
&x=\frac{-2 \pm \sqrt{0}}{2 \cdot 1}
\end{aligned}
\]

Evaluate the square root
\[
\begin{aligned}
&x=\frac{-2 \pm \sqrt{0}}{2 \cdot 1} \\
&x=\frac{-2 \pm 0}{2 \cdot 1}
\end{aligned}
\]

Add zero
\[
\begin{aligned}
&x=\frac{-2 \pm 0}{2 \cdot 1} \\
&x=\frac{-2}{2 \cdot 1}
\end{aligned}
\]

Multiply the numbers
\[
\begin{aligned}
&x=\frac{-2}{2 \cdot 1} \\
&x=\frac{-2}{2}
\end{aligned}
\]

Cancel terms that are in both the numerator and denominator
\[
\begin{aligned}
&x=\frac{-2}{2} \\
&x=-1
\end{aligned}
\]