.
Given 2x² = -8 IMPLIES
x^2 = -4 (which is -8/2),
and it means that x can not be real number.
This equation HAS NO solutions in real numbers.
It has solutions in complex number domain.
In complex number domain, equation
x^2 = -4
has two roots
x = = +/- 2i,
where " i " is complex imaginary units i = .
So, again, the original equation has no real roots;
it has two complex roots 2i and -2i.
Solved and explained.
/////////////////
On complex numbers, see introductory lessons
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Solved problems on taking roots of complex numbers
- Solved problems on arithmetic operations on complex numbers
- Solved problem on taking square root of complex number
- Solving polynomial equations in complex domain
- Miscellaneous problems on complex numbers
in this site.
Also, you have this free of charge online textbook on ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Complex numbers".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.