Question
Solve: $\text{3x}^2+5\sqrt5\text{x}-10=0$
✓
Answer
$\text{3x}^2+5\sqrt5\text{x}-10=0$$\Rightarrow\text{3x}^2+6\sqrt5\text{x}-\sqrt5\text{x}-10=0$
$\Rightarrow\text{3x}\big(\text{x}+2\sqrt5\big)-\sqrt5\big(\text{x}+2\sqrt5\big)=0$
$\Rightarrow\big(\text{x}+2\sqrt5\big)\big(\text{3x}-\sqrt5\big)=0$
$\Rightarrow\text{x}+2\sqrt5=0$ or $\text{3x}-\sqrt5=0$
$\Rightarrow\text{x}=-2\sqrt5$ or $\text{x}=\frac{\sqrt5}{3}$
$\Rightarrow\text{3x}\big(\text{x}+2\sqrt5\big)-\sqrt5\big(\text{x}+2\sqrt5\big)=0$
$\Rightarrow\big(\text{x}+2\sqrt5\big)\big(\text{3x}-\sqrt5\big)=0$
$\Rightarrow\text{x}+2\sqrt5=0$ or $\text{3x}-\sqrt5=0$
$\Rightarrow\text{x}=-2\sqrt5$ or $\text{x}=\frac{\sqrt5}{3}$
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