Solve for x
x=\sqrt[3]{\sqrt{2}-1}-\sqrt[3]{\sqrt{2}+1}\approx -0.596071638
x=0
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t^{2}+3t+2=0
Substitute t for x^{2}.
t=\frac{-3±\sqrt{3^{2}-4\times 1\times 2}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 3 for b, and 2 for c in the quadratic formula.
t=\frac{-3±1}{2}
Do the calculations.
t=-1 t=-2
Solve the equation t=\frac{-3±1}{2} when ± is plus and when ± is minus.
x\in \emptyset
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.
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