Solve the Following Quadratic Equation by Factorization
Question:
\[ 7x+\frac{3}{x}=35\frac{3}{5} \]Solution
Convert the mixed fraction into an improper fraction:
\[ 35\frac{3}{5}=\frac{178}{5} \]Therefore,
\[ 7x+\frac{3}{x}=\frac{178}{5} \]Multiplying both sides by \(5x\):
\[ 35x^2+15=178x \] \[ 35x^2-178x+15=0 \]Factorizing:
\[ 35x^2-175x-3x+15=0 \] \[ 35x(x-5)-3(x-5)=0 \] \[ (x-5)(35x-3)=0 \]Therefore,
\[ x-5=0 \] or \[ 35x-3=0 \] \[ x=5 \] or \[ x=\frac{3}{35} \]