Solve the following quadratic equation by factorization:
$7x+\frac{3}{x}=35\frac{3}{5}$

Given:

Given quadratic equation is $7x+\frac{3}{x}=35\frac{3}{5}$.

To do:

We have to solve the given quadratic equation.

Solution:

$7x+\frac{3}{x}=35\frac{3}{5}$

$\frac{7x(x)+3}{x}=35\frac{3}{5}$

$\frac{7x^2+3}{x}=35\frac{3}{5}$

$7x^2+3=(35\frac{3}{5})x$

$7x^2-35\frac{3}{5}x+3=0$

$7x^2-35x-\frac{3}{5}x+3=0$

$7x(x-5)-\frac{3}{5}(x-5)=0$

$(7x-\frac{3}{5})(x-5)=0$

$7x-\frac{3}{5}=0$ or $x-5=0$

$7x=\frac{3}{5}$ or $x=5$

$x=\frac{3}{5\times7}$ or $x=5$

$x=\frac{3}{35}$ or $x=5$

The values of $x$ are $\frac{3}{35}$ and $5$.

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Updated on: 10-Oct-2022

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