1549.73^2+((1549.73*16+x^2)/(-16+x^2))^2+1549.73*+((1549.73*16+x^2)/(-16+x^2))^2=2500^2
You asked:
Solve the equation \({1549.73}^{2} + {\left( \frac{1549.73 \cdot 16 + {x}^{2}}{-16 + {x}^{2}} \right)}^{2} + 1549.73 \cdot {\left( \frac{1549.73 \cdot 16 + {x}^{2}}{-16 + {x}^{2}} \right)}^{2} = {2500}^{2}\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= - 2 \sqrt{\frac{83353996400}{12822620657} + \frac{18 \sqrt{196858479294324756635983}}{64113103285}} \approx -22.896941\\x &= 2 \sqrt{\frac{83353996400}{12822620657} + \frac{18 \sqrt{196858479294324756635983}}{64113103285}} \approx 22.896941\\x &= - 2 \sqrt{- \frac{83353996400}{12822620657} + \frac{18 \sqrt{196858479294324756635983}}{64113103285}} i \approx -21.731672 i\\x &= 2 \sqrt{- \frac{83353996400}{12822620657} + \frac{18 \sqrt{196858479294324756635983}}{64113103285}} i \approx 21.731672 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).