SOLUTION: Please help me solve this equation in the complex number system. x^2+x+5=0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please help me solve this equation in the complex number system. x^2+x+5=0      Log On


   

Question 816063: Please help me solve this equation in the complex number system.
x^2+x+5=0
Answer by doodles(24) About Me  (Show Source):
You can put this solution on YOUR website!
Well we start off by using the quadratic equation in conjunction to the formula given.
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+
This gives us:
%28-2+%2B-+sqrt+%284-20%29%29%2F%282%29+
This then leads us to:
+%28-2+%2B-+sqrt+%28-16%29%29%2F%282%29+
and you should know since +sqrt%28-16%29+ is technically impossible to do but we can switch this to an imaginary number. So our equation would be:
+%28-2%2F2%29+%2B-+sqrt+%2816i%29%2F%282%29+
Then we further equation along by:
+%28-2%2F2%29+%2B-+%284i%29%2F+%282%29%29+
Then finally we reduce:
x+=++-1+%2B-+4i%2F2