Question

Find x if 17+12x=(x+1)^4. There are 4 possible solutions, including two complex solutions.

Answer 1

Given 17+12x=(x+1)^4
-x^4-4x^3-6x^2+8x+16=0
x = -√2
x = √2
x = -2-2i
x = -2+2i

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Comments

You haven't shown your working:
17+12x=(x+1)^4=x^4+4x^3+6x^2+4x+1.
x^4+4x^3+6x^2-8x-16=0;
(x^4+6x^2-16)+4x(x^2-2)=0;
(x^2+8)(x^2-2)+4x(x^2-2)=0;
(x^2+4x+8)(x^2-2)=0.
So x^2=2 and x=sqrt(2) or -sqrt(2), or x^2+4x+8=0.
x^2+4x+4+4=0; (x+2)^2=-4, x+2=-2i or 2i, and x=-2-2i or -2+2i.