Question

What's the answer on 4n^2 plus 12n plus 9=0

Answer 1

$4 {n}^{2} + 12n + 9 = 0 \\ 4 {n}^{2} + (6 + 6)n + 9 \\ 4 {n}^{2} + 6n + 6n + 9 \\ 2n(2n + 3) + 3(2n + 3) \\ (2n + 3)(2n + 3) \\ 2n = - 3 \\ n = - \frac{3}{2}$
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Answer 2

$\textbf{Answer :}$

Now,

4n² + 12n + 9 = 0

or, (2n)² + (2 × 2n × 3) + 3² = 0

or, (2n + 3)² = 0,

using the identity

(a + b)² = a² + 2ab + b²

or, (2n + 3) (2n + 3) = 0

∴ 2n + 3 = 0, 2n + 3 = 0

i.e., n = - 3/2, - 3/2

Hence, the required solution be

n = - 3/2, - 3/2

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