Question

find the roots of the equation 5x²-7x-6=0by the method of completing square​

Answer 1

$\large \boxed{ \tt5 {x}^{2} - 7x - 6 = 0 } \\ \\ \bold{ \rm \: multipliying \: 5 \: both \: side} \\ \\ \longmapsto \rm \: 25 {x}^{2} - 35x - 30 = 0 \\ \\ \rm \longmapsto \: (5x)^{2} - 2(5x)( \frac{7}{2} ) - 30 = 0 \\ \\ \bold{ \tt \:adding \: \: and \: \: subtrating \: 169 \div 4 \: in \: lhs } \\ \\ \longmapsto \tt \: (5x) - ^{2} - 2(5x)( \frac{7}{2} ) + \frac{ - 30}{1} + \frac{ 169}{4} - \frac{169}{4} = 0 \\ \\ \\ \longmapsto \tt \: (5x) ^{2} - 2(5x)( \frac{7}{2} ) + \frac{ - 120 + 169}{4} = \frac{169}{4} = 0 \\ \\ \\ \longmapsto \tt \: (5x) ^{2} - 2(5x)( \frac{7}{2} ) +( \frac{49}{4} ) - \frac{169}{4} = 0 \\ \\ \\ \longmapsto \tt \: (5x)^{2} - 2(5x)( \frac{7}{2} ) + ( \frac{7}{2} ^{2}) = \frac{169}{4} \\ \\ \\ \longmapsto \rm \: (5x - \frac{7}{2} ) ^{2} = \frac{169}{4} \\ \\ \\ \longmapsto \rm \: 5x - \frac{7}{2} = ± \bold{\frac{13}{2} }$