Question

resolva $x^{2}$ + x + 2=0

Answer 1

$ax^{2}+bx+c=0$

Fórmula de bhaskara:

$\boxed{x=\frac{-b\pm\sqrt{\Delta}}{2a}}\\\\\boxed{\Delta=b^{2}-4ac}$
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$x^{2}+x+2=0\\1x^{2}+1x+2=0$

$\Delta=b^{2}-4ac\\\Delta=1^{2}-4*1*2\\\Delta=1-8\\\Delta=-7\\\sqrt{\Delta}=\sqrt{-7}\\\sqrt{\Delta}=\sqrt{-1*7}\\\sqrt{\Delta}=\sqrt{-1}*\sqrt{7}\\\sqrt{\Delta}=i*\sqrt{7}$

$x=(-b\pm\sqrt{\Delta})/2a\\x=(-1\pm i\sqrt{7})/(2*1)\\x=(-1\pm i\sqrt{7})/2\\\\x'=(-1+i\sqrt{7})/2\\\\x''=(-1-i\sqrt{7})/2$

$\boxed{\boxed{S=\{\frac{-1+i\sqrt{7}}{2},~\frac{-1-i\sqrt{7}}{2}\}}}$

Se for pra resolver nos reais, a solução é vazia (as 2 raízes da equação são complexas)

Caso seja nos reais:

$\boxed{\boxed{S=\{~\}}}$