How do you solve x3 plus x2-x equals 0?

Answer 1

x^(3) +x^(2) - x = 0

Factor

x(x^(2) + x - 1) = 0

First part of the answerr is x = 0

Second part of the answer

x^(2) + x - 1 = 0

Use Quadratic Eq'n.

x = { -1 +/- sqrt[1^(2) - 4(1)(-1_]} / 2(1)

x = { -1 +/- sqrt[1 + 4]} / 2

x = ( -1 +/- sqrt)5)} / 2

x = =1 +/- 2.236...} / 2

x = -1/2 +/- 2.236.../2

X = -0.5 +/- 1.118...

x = - 1.618.... & x = 0.618....

So the three values of x that satisfy the equ'n are

x = 0 , -1.618.... & 0.618....

Answer 2

x3 + x2 - x = 0

∴ x2 + x - 1 = 0

∴ x2 + x + 0.25 = 1.25

∴ (x + 0.5)2 = 1.25

∴ x + 0.5 = ± 1.251/2

∴ x = -0.5 ± 1.251/2