SOLUTION: Find all real solutions of the quadratic equation. (Enter NONE if a solution does not exist.) x^2-{{{ sqrt( 13x ) }}} + 3= 0 i subtracted 3 and x^2 to the other side to isolate

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find all real solutions of the quadratic equation. (Enter NONE if a solution does not exist.) x^2-{{{ sqrt( 13x ) }}} + 3= 0 i subtracted 3 and x^2 to the other side to isolate      Log On


   

Question 179605: Find all real solutions of the quadratic equation. (Enter NONE if a solution does not exist.)
x^2-+sqrt%28+13x+%29+ + 3= 0
i subtracted 3 and x^2 to the other side to isolate the radical
-+sqrt%28+13x+%29+= -x^2-3
then i squared both sides of the equation to get rid of the radical and got
13x= x^4+6x^2+9 i then subtracted 13x to get all the variables on one side
x^4+6x^2-13x+9=0 i don't know how to solve the rest of the problem. I tried moving the 9 to the other side then factoring out an x and trying to factor the rest of the problem but didn't work i also tried completing the square that didn't work either

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Quartics are hard. Are you sure the x is under the radical?
Maybe it's sqrt%2813%29x, that would make it quadratic and soluble easily.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all real solutions of the quadratic equation. (Enter NONE if a solution does not exist.)
x^2-+sqrt%28+13x+%29+ + 3= 0
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x^2 - sqrt(13x) + 3 = 0
I graphed it and found it has no Real Number solution.
Cheers,
Stan H.