Question 812941
Let z = x^2. So z^2 = x^4 (square both sides)


{{{ x^4 + x^2 - 6 = 0 }}}


{{{ z^2 + z - 6 = 0 }}} Replace z with x^2 and x^4 with z^2


{{{ (z - 2)(z + 3) = 0 }}}


{{{ z - 2 = 0}}} or {{{z + 3 = 0 }}}


{{{ z = 2}}} or {{{z = -3 }}}


{{{ x^2 = 2}}} or {{{x^2 = -3 }}} Remember we let z = x^2, so make the proper replacement


{{{ x = ""+-sqrt(2)}}} or {{{x = ""+-sqrt(-3) }}}


{{{ x = sqrt(2)}}}, {{{ x = -sqrt(2)}}}, {{{x = i*sqrt(3) }}} or {{{x = -i*sqrt(3) }}}



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The four solutions are


{{{ x = sqrt(2)}}}, {{{ x = -sqrt(2)}}}, {{{x = i*sqrt(3) }}} or {{{x = -i*sqrt(3) }}}


Note: {{{i}}} is the imaginary number {{{i = sqrt(-1)}}}