SOLUTION: Could someone work this out step by step for me. I do not understand. I am lost. b^4+13b^2+36=0 Thank you so much.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Could someone work this out step by step for me. I do not understand. I am lost. b^4+13b^2+36=0 Thank you so much.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 387384: Could someone work this out step by step for me. I do not understand. I am lost.
b^4+13b^2+36=0
Thank you so much.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can say k+=+b%5E2
The equation becomes
k%5E2+%2B+13k+%2B+36+=+0
Using the quadratic formula:
k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a+=+1
b+=+13
c+=+36
k+=+%28-13+%2B-+sqrt%28+13%5E2-4%2A1%2A36+%29%29%2F%282%2A1%29+
k+=+%28-13+%2B-+sqrt%28+169+-+144+%29%29%2F2+
k+=+%28-13+%2B-+sqrt%28+25+%29%29%2F2+
k+=+%28-13+%2B+5%29%2F2
k+=+-4
and
k+=+%28-13+-+5%29%2F2
k+=+-9
And, since
k+=+b%5E2
-4+=+b%5E2
b+=+2i
and
-9+=+b%5E2
b+=+3i
The roots are imaginary
If I put b+=+3i back into the equation:
%283i%29%5E4+%2B+13%2A%283i%29%5E2+%2B+36+=+0
81+-+117+%2B+36+=+0
117+-+117+=+0
b+=+2i should check also
(note that+i%5E4+=+1)