Solve √2x² + 7x + 5√2 = 0 by Factorization
Question:
\[ \sqrt2x^2+7x+5\sqrt2=0 \]Solution
Given:
\[ \sqrt2x^2+7x+5\sqrt2=0 \]Product of the coefficient of \(x^2\) and the constant term:
\[ (\sqrt2)(5\sqrt2)=10 \]We split the middle term \(7x\) as \(5x+2x\):
\[ \sqrt2x^2+5x+2x+5\sqrt2=0 \]Taking common factors:
\[ x(\sqrt2x+5)+\sqrt2(\sqrt2x+5)=0 \] \[ (\sqrt2x+5)(x+\sqrt2)=0 \]Therefore,
\[ \sqrt2x+5=0 \quad \text{or} \quad x+\sqrt2=0 \] \[ x=-\frac{5}{\sqrt2} =-\frac{5\sqrt2}{2} \] \[ x=-\sqrt2 \]