{ x }^{ 3 } -3x-2= { \left(x+1 \right) }^{ 2 } (x-2
Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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x^{3}-3x-2=\left(x^{2}+2x+1\right)\left(x-2\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{3}-3x-2=x^{3}-3x-2
Use the distributive property to multiply x^{2}+2x+1 by x-2 and combine like terms.
x^{3}-3x-2-x^{3}=-3x-2
Subtract x^{3} from both sides.
-3x-2=-3x-2
Combine x^{3} and -x^{3} to get 0.
-3x-2+3x=-2
Add 3x to both sides.
-2=-2
Combine -3x and 3x to get 0.
\text{true}
Compare -2 and -2.
x\in \mathrm{C}
This is true for any x.
x^{3}-3x-2=\left(x^{2}+2x+1\right)\left(x-2\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
x^{3}-3x-2=x^{3}-3x-2
Use the distributive property to multiply x^{2}+2x+1 by x-2 and combine like terms.
x^{3}-3x-2-x^{3}=-3x-2
Subtract x^{3} from both sides.
-3x-2=-3x-2
Combine x^{3} and -x^{3} to get 0.
-3x-2+3x=-2
Add 3x to both sides.
-2=-2
Combine -3x and 3x to get 0.
\text{true}
Compare -2 and -2.
x\in \mathrm{R}
This is true for any x.
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