Question

Factorize the quadratic equation- 6n^2− 18n − 18 = 6

Answer 1

$\bf \large \color{pink}Hola!$

GiveN :

$\sf \mapsto \: 6 {n}^{2} - 18n - 18 = 6$

SolutioN :

$\tt \fcolorbox{skyblue}{skyblue}{Process - 1}$

$\sf \mapsto \: 6 {n}^{2} - 18n - 18 = 6$

$\implies \sf \: \cancel6( {n}^{2} - 3n - 3) = \cancel6$

$\implies \sf \: {n}^{2} - 3n - 4= 0$

$\implies \sf \: {n}^{2} - 4n + n - 4= 0$

$\implies \sf \: n({n}^{} - 4) +1 (n - 4)= 0$

$\implies \sf \: ({n}^{} - 4) (n + 1)= 0$

$\implies{ \underline{ \boxed{ \sf \: n \: = \: 4 \: \: \: \: \: \: \: \: \: \: ; \: \: \: \: \: \: \: \: x = \: - 1}}}$

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$\tt \fcolorbox{skyblue}{skyblue}{Process - 2}$

$\sf \mapsto \: 6 {n}^{2} - 18n - 18 = 6$

$\implies \sf \: \cancel6( {n}^{2} - 3n - 3) = \cancel6$

$\implies \sf \: {n}^{2} - 3n - 4= 0$

$\mapsto\: { { \boxed{\tt x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} }}} \: \: \: \: \bf[ \: Formula \: ]$

$\implies\: { { \sf n = \frac{ - ( - 3) ± \sqrt{ {( - 3)}^{2} - 4 \times (1) \times ( - 4)} }{2 \times 1} }}$

$\implies\: { { \sf n = \frac{ 3 ± \sqrt{ {25}} }{2 } }}$

$\implies{ \underline{ \boxed{ \sf \: n \: = \: 4 \: \: \: \: \: \: \: \: \: \: ; \: \: \: \: \: \: \: \: x = \: - 1}}}$

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HOPE THIS IS HELPFUL...