Question
Solve the following quadratic equation:$\sqrt2\text{x}^2+7\text{x}+5\sqrt2=0$
✓
Answer
$\sqrt2\text{x}^2+7\text{x}+5\sqrt2=0$$\Rightarrow\sqrt2\text{x}^2+5\text{x}+2\text{x}+50\sqrt2=0$
$\Rightarrow\text{x}\big(\sqrt2\text{x}+5\big)-\sqrt2\big(\sqrt2\text{x}+5\big)=0$
$\Rightarrow\big(\sqrt2\text{x}+5\big)\big(\text{x}+\sqrt2\big)=0$
$\Rightarrow\sqrt2\text{x}+5=0$ or $\text{x}+\sqrt2=0$
$\Rightarrow\text{x}=\frac{-5}{\sqrt2}$ or $\text{x}=-\sqrt2$
$\Rightarrow\text{x}\big(\sqrt2\text{x}+5\big)-\sqrt2\big(\sqrt2\text{x}+5\big)=0$
$\Rightarrow\big(\sqrt2\text{x}+5\big)\big(\text{x}+\sqrt2\big)=0$
$\Rightarrow\sqrt2\text{x}+5=0$ or $\text{x}+\sqrt2=0$
$\Rightarrow\text{x}=\frac{-5}{\sqrt2}$ or $\text{x}=-\sqrt2$
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