Question

O quadrado da metade de um número adicionado ao triplo desse número é igual a vinte e sete ?

Answer 1

$\bigg(\dfrac{k}{2}\bigg)^2+3k=27\ \to\ \dfrac{k^2}{4}+3k-27=0\ \to\ k^2+12k-108=0\\\\ k=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-12\pm\sqrt{12^2-4(1)(-108)}}{2(1)}=\\\\ =\dfrac{-12\pm\sqrt{144+432}}{2}=\dfrac{-12\pm\sqrt{576}}{2}=\dfrac{-12\pm24}{2}=-6\pm12\\\\ k=-6+12=\boxed{6}\ \ ou\ \ k=-6-12=\boxed{-18}$