Question
Solve the following quadratic equation by factorization method
$
\sqrt{2} x^2+7 x+5 \sqrt{2}=0
$
$
\sqrt{2} x^2+7 x+5 \sqrt{2}=0
$
✓
Answer
$\begin{aligned} & \sqrt{2} x^2+7 x+5 \sqrt{2}=0 \\ & \sqrt{2} x^2+2 x+5 x+5 \sqrt{2}=0 \\ & \sqrt{2} x(x+\sqrt{2})+5(x+\sqrt{2})=0\end{aligned}$
$(x+\sqrt{2})+(\sqrt{2} x+5)=0 \ldots \ldots . .($ equate the product of factors to zero)
$x+-\sqrt{2}=0$ or $\sqrt{2} x+-5$
$x=\frac{-5}{\sqrt{2}}$
The roots are $-\sqrt{2}, \frac{-5}{\sqrt{2}}$
$(x+\sqrt{2})+(\sqrt{2} x+5)=0 \ldots \ldots . .($ equate the product of factors to zero)
$x+-\sqrt{2}=0$ or $\sqrt{2} x+-5$
$x=\frac{-5}{\sqrt{2}}$
The roots are $-\sqrt{2}, \frac{-5}{\sqrt{2}}$
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