Question

What is the solution set for 2x^2+20=8

Answer 1

$2x^2+20=8\qquad|-20\\\\2x^2=-12\qquad|:2\\\\x^2=-6 < 0\\\\\text{No real solution}\\----------------------------\\\text{In complex numbers}\\\\i=\sqrt{-1}\\\\x^2=-6\to x=\pm\sqrt{-6}\\\\x=-\sqrt{(6)(-1)}\ \vee\ x=\sqrt{(6)(-1)}\\\\x=-\sqrt6\cdot\sqrt{-1}\ \vee\ x=\sqrt6\cdot\sqrt{-1}\\\\\boxed{x=-i\sqrt6\ \vee\ x=i\sqrt6}$