Question

Solve the following quadratic equation by completing the square: $\frac{5x+7}{x-1}=3x+2$

• A. $\{-1,3\}$
• B. $\{1,3\}$
• C. $\{-1,-3\}$
• D. None of these

Answer 1

The correct option is A $\{-1,3\}$

Given $\frac{5x+7}{x-1}=3x+2$

$\Rightarrow$ $5x+7=(3x+2)(x-1)$

$\Rightarrow$ $5x+7=3x^2-3x+2x-2$

$\Rightarrow$ $3x^2-6x-9=0$

$\Rightarrow$ $x^2-2x-3=0$

$\Rightarrow$ Here, $a=1,b=-2,c=-3$

$\Rightarrow$ $x^2-2x=3$

Now, ${\left(\frac{b}{2}\right)}^2={\left(\frac{-2}{2}\right)}^2=1$

Adding $1$ on both sides,

$\Rightarrow$ $x^2-2x+1=3+1$

$\Rightarrow$ $(x-1{)}^2=4$

Taking square root on both sides

$\Rightarrow$ $x-1=\pm 2$

$\Rightarrow$ $x-1=2$ and $x-1=-2$

$\therefore$ $x=3$ and $x=-1$