Question 462550
{{{(x^2 +1)^2 - 18( x^2 +1) = -17}}}

{{{x^4+2x^2 +1 - 18x^2 -1 = -17}}}

{{{x^4 -16x^2 +17=0}}}

{{{(x^2)^2 -16x^2 +17=0}}}...you can solve it as quadratic using quadratic formula, you will just have four solutions; both solutions as quadratic equation you will take positive i negative value of their square root

*[invoke quadratic_formula 1, -16, 17, "x"]
 
So yoursolutions are:

{{{x=sqrt(8+(sqrt(47))) }}} or {{{x=sqrt(8-(sqrt(47)))}}}


{{{x=sqrt(8+6.8556546) }}} or {{{x=sqrt(8-6.8556546)}}}

{{{x=sqrt(14.8556546) }}} or {{{x=sqrt(1.1443454)}}}

{{{x=3.8543}}} or {{{x=1.06974}}}

so, your solutions are:

{{{x=3.8543}}}
{{{x=-3.8543}}}
{{{x=1.06974}}}
{{{x=-1.06974}}}


{{{ graph( 500, 500, -5, 40, -20, 40, x^4 -16x^2 +17) }}}