Question
Solve the following quadratic equation:$\sqrt3\text{x}^2+\text{10x}+7\sqrt3=0$
✓
Answer
$\sqrt3\text{x}^2+\text{10x}+7\sqrt3=0$$\Rightarrow\sqrt3\text{x}^2+12\text{x}-2\text{x}-8\sqrt3=0$
$\Rightarrow\sqrt3\text{x}\big(\text{x}+4\sqrt3\big)-2\big(\text{x}+4\sqrt{3}\big)=0$
$\Rightarrow\big(\sqrt{3}\text{x}-2\big)\big(\text{x}+4\sqrt3\big)=0$
$\Rightarrow\sqrt3\text{x}-2=0$ or $\text{x}+4\sqrt3=0$
$\Rightarrow\text{x}=\frac{2}{\sqrt3}$ or $\text{x}=-4\sqrt3$
$\Rightarrow\sqrt3\text{x}\big(\text{x}+4\sqrt3\big)-2\big(\text{x}+4\sqrt{3}\big)=0$
$\Rightarrow\big(\sqrt{3}\text{x}-2\big)\big(\text{x}+4\sqrt3\big)=0$
$\Rightarrow\sqrt3\text{x}-2=0$ or $\text{x}+4\sqrt3=0$
$\Rightarrow\text{x}=\frac{2}{\sqrt3}$ or $\text{x}=-4\sqrt3$
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