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 23)  x = ±3i, ±√2
 26)  x = 4/3, (-2/3)(1 ± i√3)
Step-by-step explanation:
23) Put in standard form to make factoring easier.
 x^4 +7x^2 -18 = 0
 (x^2 +9)(x^2 -2) = 0 . . . . factors in integers
Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:
 (x -3i)(x +3i)(x -√2)(x +√2) = 0
 x = ±3i, ±√2
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26) This will be the difference of cubes after you remove the common factor.
 81x^3 -192 = 0
 3(27x^3 -64) = 0
 (3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes
The complex roots of the quadratic can be found using the quadratic formula.
 x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)
Then the three solutions to the equation are ...
 x = 4/3, (-2/3)(1 ± i√3)