다음을 풀어보세요: (40-30+x)(6aa-10x)=100aa

$$( 40 - 30 + x ) ( 6 a a - 10 x ) = 100 a a$$

a에 대한 해 (complex solution)

$$a=-i\left(3x-20\right)^{-\frac{1}{2}}\sqrt{x}\sqrt{-5x-50}$$

$$a=i\left(3x-20\right)^{-\frac{1}{2}}\sqrt{x}\sqrt{-5x-50}\text{, }x\neq \frac{20}{3}$$

x에 대한 해 (complex solution)

$$x=-\frac{\sqrt{9a^{4}-700a^{2}+2500}}{10}+\frac{3a^{2}}{10}-5$$

$$x=\frac{\sqrt{9a^{4}-700a^{2}+2500}}{10}+\frac{3a^{2}}{10}-5$$

a에 대한 해

$$a=\sqrt{\frac{5x\left(x+10\right)}{3x-20}}$$

$$a=-\sqrt{\frac{5x\left(x+10\right)}{3x-20}}\text{, }x>\frac{20}{3}\text{ or }\left(x\geq -10\text{ and }x\leq 0\right)$$

x에 대한 해

$$x=-\frac{\sqrt{9a^{4}-700a^{2}+2500}}{10}+\frac{3a^{2}}{10}-5$$

$$x=\frac{\sqrt{9a^{4}-700a^{2}+2500}}{10}+\frac{3a^{2}}{10}-5\text{, }|a|\geq \frac{5\sqrt{10}+10}{3}\text{ or }|a|\leq \frac{5\sqrt{10}-10}{3}$$