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x^2+6x-11=0

 May 4, 2015

Best Answer 

 #1
avatar+33666 
+5

This doesn't factor nicely, so you'll need to use the quadratic equation.

 

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{11}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{7.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
{\mathtt{x}} = {\mathtt{1.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
\end{array} \right\}$$

.

 May 4, 2015
 #1
avatar+33666 
+5
Best Answer

This doesn't factor nicely, so you'll need to use the quadratic equation.

 

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{11}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\mathtt{3}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{7.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
{\mathtt{x}} = {\mathtt{1.472\: \!135\: \!954\: \!999\: \!579\: \!4}}\\
\end{array} \right\}$$

.

Alan May 4, 2015

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