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\({x^2} - 5x + 6 = 0\) الف
\(9{x^2} + 3x - 2 = 0\) ب
\({x^2} + \frac{1}{4} = - x\) پ
\({x^2} + 6x + 9 = 0\) ث
الف
\(\begin{array}{l}{x^2} - 5x + 6 = 0\\\\ \Rightarrow {x^2} - 5x = - 6\\\\\frac{{ - 5}}{2} \Rightarrow {(\frac{{ - 5}}{2})^2} = \frac{{25}}{4}\\\\ \Rightarrow {x^2} - 5x + \frac{{25}}{4} = - 6 + \frac{{25}}{4}\\\\ \Rightarrow {(x - \frac{5}{2})^2} = \frac{1}{4}\\\\ \Rightarrow x - \frac{5}{2} = \pm \frac{1}{2} \Rightarrow \left\{ \begin{array}{l}x = \frac{5}{2} + \frac{1}{2} = 3\\\\x = \frac{5}{2} - \frac{1}{2} = 2\end{array} \right.\end{array}\)
ب
\(\begin{array}{l}9{x^2} + 3x - 2 = 0\\\\ \Rightarrow {x^2} + \frac{1}{3}x = \frac{2}{9}\\\\\frac{{\frac{1}{3}}}{2} = \frac{1}{6} \Rightarrow {(\frac{1}{6})^2} = \frac{1}{{36}}\\\\ \Rightarrow {x^2} + \frac{1}{3}x + \frac{1}{{36}} = \frac{2}{9} + \frac{1}{{36}}\\\\ \Rightarrow {(x + \frac{1}{6})^2} = \frac{1}{4}\\\\ \Rightarrow x + \frac{1}{6} = \pm \frac{1}{2} \Rightarrow \left\{ \begin{array}{l}x = - \frac{1}{6} + \frac{1}{2} = \frac{1}{3}\\\\x = - \frac{1}{6} - \frac{1}{2} = - \frac{2}{3}\end{array} \right.\end{array}\)
پ
\(\begin{array}{l}{x^2} + \frac{1}{4} = - x\\\\ \Rightarrow {x^2} + x + \frac{1}{4} = 0\\\\ \Rightarrow {(x + \frac{1}{2})^2} = 0\\\\ \Rightarrow x + \frac{1}{2} = 0\\\\ \Rightarrow x = - \frac{1}{2}\end{array}\)
ث
\(\begin{array}{l}{x^2} + 6x + 9 = 0\\\\ \Rightarrow {(x + 3)^2} = 0\\\\ \Rightarrow x + 3 = 0\\\\ \Rightarrow x = - 3\end{array}\)
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