28148=(204.2x)^2-(23691.8/x^2)
You asked:
Solve the equation \(28148 = {\left( 204.2 x \right)}^{2} - \frac{23691.8}{{x}^{2}}\) for the variable \(x\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}x &= \sqrt{\frac{351850}{1042441} + \frac{\sqrt{741231014595}}{1042441}} \approx 1.0786199\\x &= \sqrt{- \frac{351850}{1042441} + \frac{\sqrt{741231014595}}{1042441}} i \approx 0.69883531 i\\x &= - \sqrt{\frac{351850}{1042441} + \frac{\sqrt{741231014595}}{1042441}} \approx -1.0786199\\x &= - \sqrt{- \frac{351850}{1042441} + \frac{\sqrt{741231014595}}{1042441}} i \approx -0.69883532 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).