To solve this for x, start by rewriting x^4 + x^3 - x = 12 in descending powers of x:
x^4 + x^3 - x - 12 = 0
Next, identify possible integer factors of -12: plus or minus 1, plus or minus 2, plus or minus 3, plus or minus 4, plus or minus 6, plus or minus 12
Next, determine whether any of these are actual factors of x^4 + x^3 - x - 12 = 0 by applying synthetic division:
Check whether -2 is a root of x^4 + x^3 - x - 12 = 0:
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-2 / 1 1 -1 -12
-2 2 -2
_____ ________
1 -1 1 -14 Since there is a remainder (-14), -2 is NOT a root.
Continue this process, eliminating the possible roots one by one, until any root have been identified.
None of the possible roots proves to be an actual root.
Note that as x grows larger and larger, the given function looks more and more like f(x) = x^4 - 12, which has two real roots which are non-integer.
Please go back and ensure that you have copied this problem down correctly.
