Question

factorise it by completing the square method:
$9 {x}^{2} - 15x + 6 = 0$​

Answer 1

Step-by-step explanation:

$\huge{\bold☘}\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}$

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$factorise it by completing the square method:

$9 {x}^{2} - 15x + 6 = 0$

$\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer</p><p> }}}}}$

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$⟹\bold{9 {x}^{2} - 15x + 6 = 0}$

$⟹\bold{9 {x}^{2} - 15x = - 6}$

$⟹ \bold{{x}^{2} - \frac{15}{9} x = - \frac{6}{9}}$

$⟹\bold{ {x}^{2} - \frac{5}{3} x = - \frac{2}{3}}$

$⟹\bold{ {x}^{2} - \frac{5}{3} x + { (\frac{5}{6} )}^{2} = - \frac{2}{3} + { (\frac{5}{6} )}^{2}}$

$⟹\bold{ {(x - \frac{5}{6}) }^{2} = - \frac{2}{3} + \frac{25}{36} }$

$⟹\bold{{(x - \frac{5}{6}) }^{2} = \frac{ - 24 + 25}{36} }$

$\bold{ {(x - \frac{5}{6} )}^{2} = \frac{1}{36} = {( \frac{1}{6} )}^{2}}$

Taking square root on both sides,we get

$⟹\bold{(x - \frac{5}{6} ) = ± \frac{1}{6} }$

$⟹\bold{x - \frac{5}{6} = \frac{1}{6} }$

$⟹\bold{x - \frac{5}{6} = - \frac{1}{6} }$

$⟹\bold{x = \frac{5}{6} + \frac{1}{6} }$

$⟹\bold{x = \frac{5}{6} - \frac{1}{6}}$

$⟹\bold{\red{\boxed{x = 1}}}$

$⟹\bold{\red{\boxed{x = \frac{4}{6} = \frac{2}{3}}}}$

∴The solutions to given equation are$\bold{\red{1}}$and $\bold{\red{2/3}}$

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