5 months ago
Q:

X^2-2x-3=0

Accepted Solution

A:
${x}^{2}-3x=3$
${x}^{2}-3x+?=3+?$
${x}^{2}-3x+\frac{ 9 }{ 4 }=3+?$
${x}^{2}-3x+\frac{ 9 }{ 4 }=3+\frac{ 9 }{ 4 }$
${\left( x-\frac{ 3 }{ 2 } \right)}^{2}=3+\frac{ 9 }{ 4 }$
${\left( x-\frac{ 3 }{ 2 } \right)}^{2}=\frac{ 21 }{ 4 }$
$\begin{array} { l }x=\frac{ -\sqrt{ 21 }+3 }{ 2 },\\x=\frac{ \sqrt{ 21 }+3 }{ 2 }\end{array}$
$\begin{align*}&\begin{array} { l }x_1=\frac{ -\sqrt{ 21 }+3 }{ 2 },& x_2=\frac{ \sqrt{ 21 }+3 }{ 2 }\end{array} \\&\begin{array} { l }x_1\approx-0.791288,& x_2\approx3.79129\end{array}\end{align*}$