Question

Solve for all solutions of the equation. x3 - 8 = 0

Answer 1

x3=0+8

×3=8

x=8/3

Explanation:

Answer 2

x = 2, -1+i√3, −1−i√3

Explanation:

Factoring the left side of the equation:

x^3−2^3=0

(x−2)(x^2+x⋅2+2^2)=0

(x−2)(x^2+2x+2^2)=0

(x−2)(x^2+2x+4)=0

x−2=0

x^2+2x+4=0

First solution:

x−2=0

x=2

Second and third solution:

x^2+2x+4=0

−2±√2^2−4⋅(1⋅4)/2⋅1

x=−2±2i√3/2⋅1

x=−2±2i√3/2

−2±2i√3/2

x=−1±i√3

x=−1+i√3

x=−1−i√3

x=−1+i√3,−1−i√3

Final answer:

x=2,−1+i√3,−1−i√3