Solve the following quadratic equation by completing the square m… - Vidyadip

Question

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

✓

Answer

$
\begin{aligned}
& (3 x+2)(x-1)=5 x+7 \\
& 3 x^2-3 x+2 x-2=5 x+7 \\
& \Rightarrow 3 x^2-x-5 x-2-7=0 \\
& 3 x^2-6 x-9=0 \\
& \left.\Rightarrow x^2-2 x-3=0 \text {...(divided by } 3\right) \\
& x^2-2 x=3
\end{aligned}
$

Adding $\left(\frac{1}{2} \times 2\right)^2$ on both sides

$
\begin{aligned}
& x^2-2 x+1=3+1 \\
& (x-1)^2=4 \\
& \Rightarrow x-1=\sqrt{4} \\
& x-1= \pm 2 \\
& x-1=2 \text { or } x-1=-2 \\
& x=3 \text { or } x=-1
\end{aligned}
$
The solution set is -1 and 3

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