Find the roots of the following quadratic equ | vedclass

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(B) Given equation: $5x^{2}-4x-10=0$Divide the entire equation by $5$ to make the coefficient of $x^{2}$ equal to $1$:$x^{2}-\frac{4}{5}x-2=0$To compl

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$\frac{2-3\sqrt{6}}{5}$ and $\frac{2+3\sqrt{6}}{5}$

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(B) Given equation: $5x^{2}-4x-10=0$Divide the entire equation by $5$ to make the coefficient of $x^{2}$ equal to $1$:$x^{2}-\frac{4}{5}x-2=0$To complete the square,add and subtract the square of half the coefficient of $x$,which is $(\frac{1}{2} 	imes \frac{4}{5})^{2} = (\frac{2}{5})^{2} = \frac{4}{25}$:$x^{2}-\frac{4}{5}x + \frac{4}{25} - \frac{4}{25} - 2 = 0$$(x-\frac{2}{5})^{2} - (\frac{4}{25} + 2) = 0$$(x-\frac{2}{5})^{2} - (\frac{4+50}{25}) = 0$$(x-\frac{2}{5})^{2} - \frac{54}{25} = 0$$(x-\frac{2}{5})^{2} = \frac{54}{25}$Taking the square root on both sides:$x-\frac{2}{5} = \pm \sqrt{\frac{54}{25}} = \pm \frac{3\sqrt{6}}{5}$$x = \frac{2}{5} \pm \frac{3\sqrt{6}}{5}$$x = \frac{2 \pm 3\sqrt{6}}{5}$Therefore,the roots are $\frac{2-3\sqrt{6}}{5}$ and $\frac{2+3\sqrt{6}}{5}$.

Find the roots of the following quadratic equation by the method of completing the square: $5x^{2}-4x-10=0$

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