Answer:
NO REAL SOLUTIONS
and complex solutions: [tex]\bold{x_1=\frac{ i\,\sqrt{46}}2\ ,\quad x_2=-\frac{ i\,\sqrt{46}}2}[/tex]
Step-by-step explanation:
-27 = 2x² - 4
-2x² = 27 - 4
-2x² = 23
x² = -23/2
means NO REAL SOLUTIONS
(as there is no real number that put instead of x gives value less then 0)
However in complex numbers we have:
[tex]x=\pm\sqrt{-\frac{23}2}=\pm\sqrt{\frac{23}2}\cdot i=\pm\, i\sqrt{\frac{46}4}=\pm\frac{ i\,\sqrt{46}}2\\\\ x_1=\frac{ i\,\sqrt{46}}2\ ,\quad x_2=-\frac{ i\,\sqrt{46}}2[/tex]
