SOLUTION: Solve over the set of complex numbers. Use completing the square. 8x^2-x-1=0 (the x on first term is squared) Thank you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve over the set of complex numbers. Use completing the square. 8x^2-x-1=0 (the x on first term is squared) Thank you      Log On


   

Question 215532: Solve over the set of complex numbers. Use completing the square.
8x^2-x-1=0 (the x on first term is squared)
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
8x^2 - x - 1 = 0
:
8x^2 - x = 1
:
The coefficient of x^2 has to be 1, divide all terms by 8
x^2 - 1%2F8x = 1%2F8
:
x^2 - 1%2F8x + ___ = 1%2F8
Find the 3rd term that completes the square, divide the coefficient of x by 2
then square it; that would be (-1/16)^2, which is 1%2F256, add to both sides
x^2 - 1%2F8x + 1%2F256 = 1%2F8 + 1%2F256
x^2 - 1%2F8x + 1%2F256 = 32%2F256 + 1%2F256
x^2 - 1%2F8x + 1%2F256 = 33%2F256
which is:
(x - 1%2F16)^2 = 33%2F256
Find the square root of both sides
x - 1%2F16 = +/-sqrt%2833%2F256%29
:
We can extract the square root of (1/256) which is 1/16
x - 1%2F16 = +/-%281%2F16%29sqrt%2833%29
:
Add 1/16 to both sides
x = 1%2F16 +/-%281%2F16%29sqrt%2833%29
;
From this we can write the two solutions as:
x = %281+%2B+sqrt%2833%29%29%2F16
and
x = %281+-+sqrt%2833%29%29%2F16
;
Did you understand what went on here? Let me know, ankor@att.net