SOLUTION: I am stuck... this is a quad root problem {{{ 4sqrt(4-5x^2)=x }}} I tried {{{ 4-5x^2=x^4 }}} {{{ x=sqrt4-x^4/5 }}} Thanks

Algebra ->  Radicals -> SOLUTION: I am stuck... this is a quad root problem {{{ 4sqrt(4-5x^2)=x }}} I tried {{{ 4-5x^2=x^4 }}} {{{ x=sqrt4-x^4/5 }}} Thanks      Log On


   

Question 752094: I am stuck... this is a quad root problem
+4sqrt%284-5x%5E2%29=x+
I tried +4-5x%5E2=x%5E4+
+x=sqrt4-x%5E4%2F5+
Thanks
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
+4sqrt%284-5x%5E2%29=x+

Square both sides.
16%2A%284-5x%5E2%29=x%5E2

Distribute the multiplication by 16.
16%2A4-16%2A5x%5E2=x%5E2

continuing,...

16%2A5x%5E2-16%2A4=-x%5E2
16%2A5x%5E2%2Bx%5E2-16%2A4=0
%2816%2A5%2B1%29x%5E2-16%2A4=0
81x%5E2-64=0
81x%5E2=64
x%5E2=64%2F81
highlight%28x=8%2F9%29 or highlight%28x=-%288%2F9%29%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+4sqrt%284-5x%5E2%29=x+
I tried +4-5x%5E2=x%5E4+
:
right here you can rearrange it as a quadratic equation
0 = x^4 + 5x^2 - 4
Solve for x^2 using the quadratic formula, then find x, check the
solutions in the original equation, Only 1 solution works x ~ .8376