Question

Solve each of the following equations by the
method of completing the square.
3x2 -5 X- 1 = 0​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore x=\pm\frac{\sqrt{37}+5}{6}}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies x \in ( {3 x }^{2} - 5x - 1 = 0) \\ \\ \underline \bold{To \: Find: } \\ \implies x = ?$

• According to given question :

$\bold{Using \: method \: completing \: square : } \\ \implies {3x}^{2} - 5x - 1 = 0 \\ \\ \bold{Dividing \: whole \: equation \: by \: coefficient \: of \: {x}^{2} } \\ \implies {x}^{2} - \frac{5x}{3} - \frac{1}{3} = 0 \\ \\ \bold{Adding \: both \: side \: (\frac{b}{2a})^{2} = \frac{25}{36} }$$\\ \implies {x}^{2} - \frac{5x}{3} + \frac{25}{36} - \frac{1}{3} = \frac{25}{36} \\ \\ \implies {x}^{2} - \frac{5x}{3} + \frac{25}{36} = \frac{25}{36} + \frac{1}{3} \\ \\ \implies ({x - \frac{5}{6} })^{2} = \frac{25 + 12}{36} \\ \\ \implies x - \frac{5}{6} = \pm \sqrt{ \frac{37}{36} }$$\\\bold{\implies x=\pm\frac{\sqrt{37}+5}{6}}$

Answer 2

$\implies {3x}^{2} - 5x - 1 = 0 \\ \\ \bold{dividing \: whole \: equation \: by \: coefficient \: of \: {x}^{2} } \\ \implies {x}^{2} - \frac{5x}{3} - \frac{1}{3} = 0 \\ \\ \bold{adding \: both \: side \: (\frac{b}{2a})^{2} = \frac{25}{18} } \\ \\ \implies {x}^{2} - \frac{5x}{3} + \frac{25}{18} - \frac{1}{3} = \frac{25}{18} \\ \\ \implies {x}^{2} - \frac{5x}{3} + \frac{25}{18} = \frac{25}{18} + \frac{1}{3} \\ \\ \implies ({x - \frac{5}{6} })^{2} = \frac{25 + 6}{18} \\ \\ \implies x - \frac{5}{6} = \pm \sqrt{ \frac{31}{18} } \\ \\ \bold{\implies x = \pm \sqrt{ \frac{31}{18} } + \frac{5}{6} }$