Question

Please split this by Splitting Method....

Answer 1

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$- 2 {n}^{2} + n \: + 45 = 0 \\ = > {2n}^{2} - n \: - 45 = 0 \\ = > 2 {n}^{2} - (10 - 9)n \: - 45 = 0 \\ = > 2 {n}^{2} - 10n + 9n - 45 = 0 \\ = > 2n(n - 5) + 9(n - 5) = 0 \\ = > (2n + 9)(n - 5) = 0$

$2n \: + 9 = 0 \\ = > 2n = - 9 \\ = > n = \frac{ - 9}{2}$

$n - 5 = 0 \\ = > n = 5$

$\huge\bold{Answer = \frac{ - 9}{2} \: and \: 5}$

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Answer 2

$\huge{\boxed{\boxed{\underline{\bf SOLUTION}}}}$

It is given that,

$45 + n - 2 {n}^{2}$

We can arrange it as :

$- 2 {n}^{2} + n + 45$

$2 {n}^{2} - n - 45$

Now we shall solve it by middle term splitting or middle term factorisation.

$2 {n}^{2} - (10 - 9)n - 45$

$2 {n}^{2} - 10n + 9n - 45$

Take out the common terms

$2n(n - 5) + 9(n - 5)$

$(n - 5)(2n + 9)$

To find the factors, we have to equate them with zero.

$n - 5 = 0 \\ n = 5$

Similarly,

$2n + 9 = 0$

$2n = - 9$

$n = \frac{ - 9}{2}$

Hence,

$the \: factors \: are \: 5 \: and \: \frac{ - 9}{2}$