5 { \left( { x }_{ 1 } \right) }^{ 2 } +8 { x }_{ 1 } { x }_{ 2 } -2 { x }_{ 2 } { x }_{ 3 } -3 { x }_{ 1 } { x }_{ 3 } -3 { \left( { x }_{ 3 } \right) }^{ 2 } +13 { \left( { x }_{ 2 } \right) }^{ 2 } =0
Solve for x_1 (complex solution)
x_{1}=\frac{\sqrt{69x_{3}^{2}-8x_{2}x_{3}-196x_{2}^{2}}}{10}+\frac{3x_{3}}{10}-\frac{4x_{2}}{5}
x_{1}=-\frac{\sqrt{69x_{3}^{2}-8x_{2}x_{3}-196x_{2}^{2}}}{10}+\frac{3x_{3}}{10}-\frac{4x_{2}}{5}
Solve for x_2 (complex solution)
x_{2}=\frac{\sqrt{40x_{3}^{2}+31x_{1}x_{3}-49x_{1}^{2}}+x_{3}-4x_{1}}{13}
x_{2}=\frac{-\sqrt{40x_{3}^{2}+31x_{1}x_{3}-49x_{1}^{2}}+x_{3}-4x_{1}}{13}
Solve for x_1
x_{1}=\frac{\sqrt{69x_{3}^{2}-8x_{2}x_{3}-196x_{2}^{2}}}{10}+\frac{3x_{3}}{10}-\frac{4x_{2}}{5}
x_{1}=-\frac{\sqrt{69x_{3}^{2}-8x_{2}x_{3}-196x_{2}^{2}}}{10}+\frac{3x_{3}}{10}-\frac{4x_{2}}{5}\text{, }x_{2}\geq -\frac{\sqrt{3385}|x_{3}|}{98}-\frac{x_{3}}{49}\text{ and }x_{2}\leq \frac{\sqrt{3385}|x_{3}|}{98}-\frac{x_{3}}{49}
Solve for x_2
x_{2}=\frac{\sqrt{40x_{3}^{2}+31x_{1}x_{3}-49x_{1}^{2}}+x_{3}-4x_{1}}{13}
x_{2}=\frac{-\sqrt{40x_{3}^{2}+31x_{1}x_{3}-49x_{1}^{2}}+x_{3}-4x_{1}}{13}\text{, }x_{1}\geq \frac{-\sqrt{8801}|x_{3}|+31x_{3}}{98}\text{ and }x_{1}\leq \frac{\sqrt{8801}|x_{3}|+31x_{3}}{98}
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