Question

3x^2-x-2=0 by complete square method​

Answer 1

D=9

Step-by-step explanation:

3x²-x-2=0

D= b²-4ac

D= 1²-4x1x-2

D=1+8

D=9

Answer 2

${3x}^{2} - x - 2 = 0\\ \\ = > {( \sqrt{3}x )}^{2} + 2( \sqrt{3}x )( \frac{ - 1}{2 \sqrt{3} } ) + { \large{(}} \frac{ - 1}{2 \sqrt{3} } )^{2} - ( \frac{ - 1}{2 \sqrt{3} } )^{2} - 2 \\ \\ = > ( \sqrt{3 }x - \frac{1}{2 \sqrt{3} } )^{2} - \frac{1}{12} - 2 \\ = > { \huge{( }}\sqrt{3}x - \frac{1}{2 \sqrt{3} } { \huge{)}}^{2} - 1{ \huge{(}}\frac{1 + 24}{12} { \huge{)}} \\ \\ = > { \huge{( }}\sqrt{3}x - \frac{1}{2 \sqrt{3} } { \huge{)}}^{2} - 1( \frac{25}{12}) \\ \\ = > { \huge{( }}\sqrt{3}x - \frac{1}{2 \sqrt{3} } { \huge{)}}^{2} - \frac{25}{12} \\ \\ = > { \huge{( }}\sqrt{3}x - \frac{1}{2 \sqrt{3} } { \huge{)}}^{2} - { \large{( }}\frac{5}{2 \sqrt{3} } { \large{)}}^{2} \\ \\ = > { \huge{( }}\sqrt{3}x - \frac{1}{2 \sqrt{3} } - \frac{5}{2 \sqrt{3} } { \huge{)}}{ \huge{(}} \sqrt{3} x - \frac{1}{2 \sqrt{3} } + \frac{5}{2 \sqrt{3} } { \huge{)}} \\ \\ = > { \huge{(}} \sqrt{3}x - 1( \frac{1}{2 \sqrt{3} } + \frac{5}{2 \sqrt{3} } ){ \huge{)}}{ \huge{(}} \sqrt{3}x + \frac{ - 2 \sqrt{3} + 10 \sqrt{3} }{2 \sqrt{3} } { \huge{)}} \\ \\ = > { \huge{(}} \sqrt{3} x - \frac{11 \sqrt{3} }{2 \sqrt{3} } { \huge{)}}{ \huge{(}} \sqrt{3}x + \frac{8 \sqrt{3} }{2 \sqrt{3} } { \huge{)}} \\ \\ = > ( \sqrt{3}x - \frac{11}{2} )( \sqrt{3} x + \frac{8}{2} ) \\ \\ = > ( \sqrt{3} x - 5.5)( \sqrt{3}x + 4 ) = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \:{ \boxed{x = \frac{5.5}{ \sqrt{3} } \: \: or \: \: \frac{4}{ \sqrt{3} }}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > { \boxed{ \red{ \frac{5.5 \sqrt{3} }{9} \: \: or \frac{4 \sqrt{3} }{9} }}}$