Question

2x^2-5x/6+1/12 factorise

Answer 1

Step-by-step explanation:

$2 {x}^{2} - \frac{5x}{6} + \frac{1}{12}$

divide all terms by 2

$\frac{ {2x}^{2} }{2} - \frac{ \frac{5x}{6} }{2} + \frac{ \frac{1}{12} }{2}$

${x}^{2} - \frac{5x}{12} + \frac{1}{24} = 0$

${x}^{2} - 2 \times x \times \frac{5}{24} + {( \frac{5}{24} })^{2} - ({ \frac{5}{24} })^{2} + \frac{1}{24}$

$(x - \frac{5}{24} ) {}^{2} - ( \frac{5}{24} ) {}^{2} + \frac{1}{24}$

$(x - \frac{5}{24} ) {}^{2} - \frac{25}{576} + \frac{1}{24}$

$(x - \frac{5}{24} ) {}^{2} = \frac{25}{576} - \frac{1}{24}$

LCM of 576 and 24 is 576

$(x - \frac{5}{24} ) {}^{2} = ( \frac{25 - 24}{576} )$

$(x - \frac{5}{24} ) {}^{2} = \frac{1}{576}$

$x - \frac{5}{24} = \sqrt{ \frac{1}{576} }$

$x - \frac{5}{24} = \frac{1}{24}$

$x = \frac{5}{24} + \frac{1}{24}$

$x = \frac{6}{24} = \frac{1}{4}$