Question 481460
You can use a temporary substitution in which {{{z = x^2}}}, so...
{{{x^4+10x^2+9 = 0}}} Substitute {{{z = x^2}}}
{{{z^2+10z+9 = 0}}} Factor.
{{{(z+1)(z+9) = 0}}} Apply the "zero product" rule.
{{{z+1 = 0}}} or {{{z+9 = 0}}} so that...
{{{z = -1}}} or {{{z = -9}}} Now replace the temporary variable z with {{{z = x^2}}} to get:
{{{x^2 = -1}}} or {{{x^2 = -9}}} and so...
{{{x = sqrt(-1)}}}, {{{x = -sqrt(-1)}}}, or {{{x = sqrt(-9)}}}, {{{x = -sqrt(-9)}}} But these can be simplified to...
{{{x = i}}}, {{{x = -i}}} or {{{x = 3i}}}, {{{x = -3i}}} where {{{i = sqrt(-1)}}}