Answer:
(1/4)(1 ±i√7)
Step-by-step explanation:
The equation can be simplified to a quadratic form, then solved using the quadratic formula.
Standard form
Eliminating parentheses, we have ...
(x -1)³ -x²(x +3) = 2
x³ -3x² +3x -1 -x³ -3x² = 2 . . . . eliminate parentheses
-6x² +3x -3 = 0 . . . . . . . . . . . subtract 2, collect terms
2x² -x +1 = 0 . . . . . . . . . . divide by -3
Solution
The solution can be found using the quadratic formula. It tells us the solution to ax² +bx +c = 0 is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(1)}}{2(2)}=\dfrac{1\pm\sqrt{-7}}{4}\\\\\boxed{x=\left\{\dfrac{1}{4}-\dfrac{\sqrt{7}}{4}i,\ \dfrac{1}{4}+\dfrac{\sqrt{7}}{4}i\right\}}[/tex]
