Question

Não utilize a fórmula da equação do 2° grau.

a) x^2 + 5x + 6= 0​

Answer 1

$2x^{2}+5x+6=0 \\ 2x^{2}+5x+6-6=-6 \\ 2x^{2}+5x=-6 \\ \frac{2x^{2}+5x}{2}=\frac{-6}{2} \\ x^{2}+\frac{5}{2}x=\frac{-6}{2} \\ x^{2}+\frac{5}{2}x=-3 \\ x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=-3+\left(\frac{5}{4}\right)^{2} \\ x^{2}+\frac{5}{2}x+\frac{25}{16}=-3+\frac{25}{16} \\ x^{2}+\frac{5}{2}x+\frac{25}{16}=-\frac{23}{16} \\ \left(x+\frac{5}{4}\right)^{2}=-\frac{23}{16} \\ \sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{-\frac{23}{16}} \\ x+\frac{5}{4}=\frac{\sqrt{23}i}{4} x+\frac{5}{4}=-\frac{\sqrt{23}i}{4} \\ x=\frac{-5+\sqrt{23}i}{4} x=\frac{-\sqrt{23}i-5}{4}$

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