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

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on Nov 18, 2024 at 8:43 am



You asked:

Solve the equation 1549.732+(1549.73⋅16+x2−16+x2)2+1549.73(1549.73⋅16+x2−16+x2)2=25002{1549.73}^{2} + {\left( \frac{1549.73 \cdot 16 + {x}^{2}}{-16 + {x}^{2}} \right)}^{2} + 1549.73 {\left( \frac{1549.73 \cdot 16 + {x}^{2}}{-16 + {x}^{2}} \right)}^{2} = {2500}^{2} for the variable xx.

MathBot Answer:

The 4 solutions to the equation are: x=−28335399640012822620657+1819685847929432475663598364113103285≈−22.896941x=28335399640012822620657+1819685847929432475663598364113103285≈22.896941x=−2−8335399640012822620657+1819685847929432475663598364113103285i≈−21.731672ix=2−8335399640012822620657+1819685847929432475663598364113103285i≈21.731672i\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}

ii is the imaginary unit, defined as i2=−1i^2 = -1.

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