Question

(x-1)^3-x^2(x+3)=2

Find x
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Answer 1

(1/4)(1 ±i√7)

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 ...

`x=(-b\pm√(b^2-4ac))/(2a)=(-(-1)\pm√((-1)^2-4(2)(1)))/(2(2))=(1\pm√(-7))/(4)\\\\\boxed{x=\left\{(1)/(4)-(√(7))/(4)i,\ (1)/(4)+(√(7))/(4)i\right\}}`