Answer:
x = 2, -1+i√3, −1−i√3
Step-by-step 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
