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Quiero que me ayuden a resolver paso a paso este ejercicio!! (x- 3/2)² = 1/3 - 2/9
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![\textbf{Resolvemos:} \\ \\ \left(x- \dfrac{3}{2} \right)^{2} = \dfrac{1*3}{3*3} - \dfrac{2}{9} \\ \\ \\ x^{2}- \dfrac{6x}{2}+\dfrac{9}{4} = \dfrac{3}{9}-\dfrac{2}{9} \\ \\ \\ x^{2} -\dfrac{6x}{9}+\dfrac{9}{4} =\dfrac{1}{9}\\ \\ \\x^{2}-\dfrac{6x}{9}+ \dfrac{9}{4} -\dfrac{1}{9}\\ \\ \\ x^{2}-\dfrac{6x}{9}- \dfrac{77}{36} = 0 \\ \\ \\ Aplicamos\ la\ f\'ormula\ general: \\ \\ \boxed{ x_{1,2}= \frac{-b\ñ \sqrt{ b^{2}-4ac}}{2a}} \textbf{Resolvemos:} \\ \\ \left(x- \dfrac{3}{2} \right)^{2} = \dfrac{1*3}{3*3} - \dfrac{2}{9} \\ \\ \\ x^{2}- \dfrac{6x}{2}+\dfrac{9}{4} = \dfrac{3}{9}-\dfrac{2}{9} \\ \\ \\ x^{2} -\dfrac{6x}{9}+\dfrac{9}{4} =\dfrac{1}{9}\\ \\ \\x^{2}-\dfrac{6x}{9}+ \dfrac{9}{4} -\dfrac{1}{9}\\ \\ \\ x^{2}-\dfrac{6x}{9}- \dfrac{77}{36} = 0 \\ \\ \\ Aplicamos\ la\ f\'ormula\ general: \\ \\ \boxed{ x_{1,2}= \frac{-b\ñ \sqrt{ b^{2}-4ac}}{2a}}](https://tex.z-dn.net/?f=%5Ctextbf%7BResolvemos%3A%7D+%5C%5C+%5C%5C+%5Cleft%28x-+%5Cdfrac%7B3%7D%7B2%7D+%5Cright%29%5E%7B2%7D++%3D+%5Cdfrac%7B1%2A3%7D%7B3%2A3%7D+-++%5Cdfrac%7B2%7D%7B9%7D+%5C%5C+%5C%5C+%5C%5C++x%5E%7B2%7D-+%5Cdfrac%7B6x%7D%7B2%7D%2B%5Cdfrac%7B9%7D%7B4%7D+%3D+%5Cdfrac%7B3%7D%7B9%7D-%5Cdfrac%7B2%7D%7B9%7D+%5C%5C+%5C%5C+%5C%5C++x%5E%7B2%7D+-%5Cdfrac%7B6x%7D%7B9%7D%2B%5Cdfrac%7B9%7D%7B4%7D+%3D%5Cdfrac%7B1%7D%7B9%7D%5C%5C+%5C%5C+%5C%5Cx%5E%7B2%7D-%5Cdfrac%7B6x%7D%7B9%7D%2B++%5Cdfrac%7B9%7D%7B4%7D+-%5Cdfrac%7B1%7D%7B9%7D%5C%5C+%5C%5C+%5C%5C+x%5E%7B2%7D-%5Cdfrac%7B6x%7D%7B9%7D-+%5Cdfrac%7B77%7D%7B36%7D+%3D+0+%5C%5C+%5C%5C+%5C%5C+Aplicamos%5C+la%5C+f%5C%27ormula%5C+general%3A+%5C%5C+%5C%5C+%5Cboxed%7B+x_%7B1%2C2%7D%3D+%5Cfrac%7B-b%5C%C3%B1+%5Csqrt%7B+b%5E%7B2%7D-4ac%7D%7D%7B2a%7D%7D++++++++++++++)
![x_{1,2} =\dfrac{ -\left(-\dfrac{6}{9}\right)\ñ \sqrt{\left(- \dfrac{6}{9}\right)^{2} -\not{4}(1)\left( \dfrac{-77}{\not{36}} \right)}}{2(1)} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{36}{81}+\dfrac{308}{9}}}{2} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{104}{3}}}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ \\ x_{1} = \dfrac{ \dfrac{6}{9} + \dfrac{ \sqrt{104} }{ \sqrt{3}}}{2} = \dfrac{ 6\sqrt{3}+18\sqrt{26} }{2} \\ \\ \\
x_{2} = \dfrac{6 \sqrt{3}- 18\sqrt{26} }{2} x_{1,2} =\dfrac{ -\left(-\dfrac{6}{9}\right)\ñ \sqrt{\left(- \dfrac{6}{9}\right)^{2} -\not{4}(1)\left( \dfrac{-77}{\not{36}} \right)}}{2(1)} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{36}{81}+\dfrac{308}{9}}}{2} \\ \\ \\ x_{1,2}=\dfrac{ \dfrac{6}{9}\ñ \sqrt{\dfrac{104}{3}}}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ \\ x_{1} = \dfrac{ \dfrac{6}{9} + \dfrac{ \sqrt{104} }{ \sqrt{3}}}{2} = \dfrac{ 6\sqrt{3}+18\sqrt{26} }{2} \\ \\ \\
x_{2} = \dfrac{6 \sqrt{3}- 18\sqrt{26} }{2}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D+%3D%5Cdfrac%7B+-%5Cleft%28-%5Cdfrac%7B6%7D%7B9%7D%5Cright%29%5C%C3%B1+%5Csqrt%7B%5Cleft%28-+%5Cdfrac%7B6%7D%7B9%7D%5Cright%29%5E%7B2%7D+-%5Cnot%7B4%7D%281%29%5Cleft%28+%5Cdfrac%7B-77%7D%7B%5Cnot%7B36%7D%7D+%5Cright%29%7D%7D%7B2%281%29%7D+%5C%5C+%5C%5C+%5C%5C+x_%7B1%2C2%7D%3D%5Cdfrac%7B+%5Cdfrac%7B6%7D%7B9%7D%5C%C3%B1+%5Csqrt%7B%5Cdfrac%7B36%7D%7B81%7D%2B%5Cdfrac%7B308%7D%7B9%7D%7D%7D%7B2%7D+%5C%5C+%5C%5C+%5C%5C+x_%7B1%2C2%7D%3D%5Cdfrac%7B+%5Cdfrac%7B6%7D%7B9%7D%5C%C3%B1+%5Csqrt%7B%5Cdfrac%7B104%7D%7B3%7D%7D%7D%7B2%7D+%5C%5C+%5C%5C+Tenemos%5C+dos%5C+soluciones%3A+%5C%5C+%5C%5C+%5C%5C+x_%7B1%7D+%3D+%5Cdfrac%7B+%5Cdfrac%7B6%7D%7B9%7D+%2B++%5Cdfrac%7B+%5Csqrt%7B104%7D+%7D%7B+%5Csqrt%7B3%7D%7D%7D%7B2%7D+%3D+%5Cdfrac%7B+6%5Csqrt%7B3%7D%2B18%5Csqrt%7B26%7D++%7D%7B2%7D+%5C%5C+%5C%5C+%5C%5C+%0Ax_%7B2%7D+%3D+%5Cdfrac%7B6+%5Csqrt%7B3%7D-+18%5Csqrt%7B26%7D++%7D%7B2%7D++)
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