Let [tex]u= x^{2} [/tex] so our equation becomes [tex]u^{2}-4u+2=0[/tex] subtract 2 from both sides of the equation [tex]u^{2}-4u = -2[/tex] Take half of b, square the result and add to both sides [tex]\frac{1}{2}(-4) = -2[/tex] (remember -2 it will be used when factoring the trinomial) (-2)² = 4 [tex]u^{2}-4u+4=-2+4[/tex] Factor trinomial and simplify right side [tex](u-2)^{2}=2[/tex] note:-2 is in the factor Square root both sides (must use +/-): [tex]u-2=+/- \sqrt{2} [/tex] Add 2 to both sides: [tex]u = 2 +/- \sqrt{2} [/tex] :-( not finish yet [tex]u= x^{2} [/tex] [tex]2+ \sqrt{2} = x^{2} [/tex] and [tex]2- \sqrt{2} = x^{2} [/tex] Final answers: [tex]x= +/-\sqrt{2+ \sqrt{2}} [/tex] and [tex]x = +/-\sqrt{2- \sqrt{2} }[/tex] [tex]\sqrt{2+\sqrt{2}},-\sqrt{2+\sqrt{2}},\sqrt{2-\sqrt{2}},-\sqrt{2-\sqrt{2}}[/tex]
