Question
Find the solution of the quadratic equation $3\sqrt3\text{x}^2+\text{10x}+\sqrt3=0.$
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Answer
$3\sqrt3\text{x}^2+\text{10x}+\sqrt3=0$ $\Rightarrow3\sqrt3\text{x}^2+\text{9x}+\text{x}+\sqrt3=0$ $\Rightarrow3\sqrt3\big(\text{x}+\sqrt3\big)+1\big(\text{x}+\sqrt3\big)=0$ $\Rightarrow\big(\text{x}+\sqrt3\big)\big(3\sqrt3+1\big)=0$ $\Rightarrow\text{x}+\sqrt3=0$ or $3\sqrt3+1=0$ $\Rightarrow\text{x}=-\sqrt3$ or $\text{x}=-\frac{1}{3\sqrt3}$
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