Explicação passo-a-passo:
∆= (-6)² - 4.1.(-27)
∆= 36 + 108
∆= 144
x= - (-6) ±√144/2.1
x= 6 ± 12/2
x1= 6+12/2= 18/2= 9
x2= 6-12/2= - 6/2= -3
S = { - 3, 9 }
[tex]\large\displaystyle\text{$\rm x^2-6x-27=0 $}[/tex]
[tex]\large\displaystyle\text{$\rm \Delta=b^2-4\cdot a\cdot c $}[/tex]
[tex]\large\displaystyle\text{$\rm \Delta= (-6)^2-4\cdot1\cdot(-27)$}[/tex]
[tex]\large\displaystyle\text{$\rm\Delta=36+108 $}[/tex]
[tex]\large\displaystyle\text{$\rm\Delta=144$}[/tex]
[tex]\large\displaystyle\text{$\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}$}[/tex]
[tex]\large\displaystyle\text{$\rm x=\dfrac{-(-6)\pm\sqrt{144}}{2\cdot1} $}[/tex]
[tex]\large\displaystyle\text{$\rm x=\dfrac{6\pm12}{2}\begin{cases}\rm x_1=\dfrac{6+12}{2}=\dfrac{18}{2}=9\\\\\rm x_2=\dfrac{6-12}{2}=\dfrac{-6}{2}=-3\end{cases} $}[/tex]
[tex]\large\displaystyle\text{$\boxed{\boxed{\rm S=\{-3;9\}}} $}[/tex]
