0.613=(8x^2*0.3^0.5)/((4x^2-8x+3)^0.5*(1-2x)*8.314^0.5*300^0.5)

asked by guest
on Nov 17, 2024 at 1:55 pm



You asked:

Solve the equation \(0.613 = \frac{8 \cdot {x}^{2} \cdot {0.3}^{0.5}}{{\left( 4 \cdot {x}^{2} - 8 x + 3 \right)}^{0.5} \cdot \left(1 - 2 x\right) \cdot {8.314}^{0.5} \cdot {300}^{0.5}}\) for the variable \(x\).

MathBot Answer:

The complex solutions are: \[\left\{- \frac{\sqrt{- 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + \frac{821687082255207763}{1622549208070415526} + \frac{432189562904471087610821093}{1687528769941460490451284372 \sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}}}{2} + \frac{\sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}{2} + \frac{1562071733}{2080095644}, - \frac{\sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}{2} + \frac{1562071733}{2080095644} - \frac{i \sqrt{- \frac{821687082255207763}{1622549208070415526} - \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{432189562904471087610821093}{1687528769941460490451284372 \sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}}}{2}, - \frac{\sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}{2} + \frac{1562071733}{2080095644} + \frac{i \sqrt{- \frac{821687082255207763}{1622549208070415526} - \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{432189562904471087610821093}{1687528769941460490451284372 \sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}}}{2}, \frac{\sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + \frac{821687082255207763}{1622549208070415526} + \frac{432189562904471087610821093}{1687528769941460490451284372 \sqrt{\left|{- \frac{390517933250000}{2433823812105623289 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}}} + 2 \sqrt[3]{- \frac{38126064047462863890625}{7593879464736572207030779674} + \frac{14961718317640625 \sqrt{6626556194081}}{7593879464736572207030779674}} + \frac{821687082255207763}{3245098416140831052}}\right|}}}}{2} + \frac{1562071733}{2080095644}\right\} \setminus \left\{\frac{1}{2}, \frac{3}{2}\right\}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

+ Submit Question