Solve the quadratic equation 25 x^{2}-30 x+3= | vedclass

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Question

(C) To solve $25 x^{2}-30 x+3=0$ by completing the square,we first isolate the constant term: $25 x^{2}-30 x = -3$.Divide the entire equation by $25$

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) To solve $25 x^{2}-30 x+3=0$ by completing the square,we first isolate the constant term: $25 x^{2}-30 x = -3$.Divide the entire equation by $25$ to make the coefficient of $x^2$ equal to $1$: $x^{2} - \frac{30}{25} x = -\frac{3}{25}$,which simplifies to $x^{2} - \frac{6}{5} x = -\frac{3}{25}$.To complete the square,add $(\frac{1}{2} 	imes 	ext{coefficient of } x)^2 = (\frac{1}{2} 	imes -\frac{6}{5})^2 = (-\frac{3}{5})^2 = \frac{9}{25}$ to both sides:$x^{2} - \frac{6}{5} x + \frac{9}{25} = -\frac{3}{25} + \frac{9}{25}$.This gives $(x - \frac{3}{5})^2 = \frac{6}{25}$.Taking the square root of both sides: $x - \frac{3}{5} = \pm \frac{\sqrt{6}}{5}$.Therefore,$x = \frac{3}{5} \pm \frac{\sqrt{6}}{5}$,which results in $x = \frac{3 \pm \sqrt{6}}{5}$.Thus,the roots are $\frac{3-\sqrt{6}}{5}$ and $\frac{3+\sqrt{6}}{5}$.

Solve the quadratic equation $25 x^{2}-30 x+3=0$ by using the method of completing the square.

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