Question

$$3x+ { x }^{ 2 } =7x+ { 5 }^{ x }$$

Answer

x=-0.17929763793945

Solution


Move all terms to one side.
\[3x+{x}^{2}-7x-{5}^{x}=0\]
Simplify  \(3x+{x}^{2}-7x-{5}^{x}\)  to  \(-4x+{x}^{2}-{5}^{x}\).
\[-4x+{x}^{2}-{5}^{x}=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=-0.179298\]