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We have to solve for x given 64x^3+1331=0

64x^3 + 1331 = 0

=> (4x)^3 + 11^3 = 0

=> (4x + 11)( (4x)^2 - 4x*11 + 11^2) = 0

4x + 11 = 0 => x1 = -11/4

=> x = -2.75

( (4x)^2 - 4x*11 + 11^2) = 0

x2 = [44 + sqrt( 44^2 - 4*11^2*16)]/32

=> x2 = 44/32 + i*2.3815

=> x2 = 11/8 + i*2.3815

=> x2 = 1.375 + i*2.3815

x3 = x2 = [44 - sqrt( 44^2 - 4*11^2*16)]/32

=> x3 = 11/8 - i*2.3815

=> x3 = 1.375 - i*2.3815

The values of x are -2.75 , 1.375 + i*2.3815 , 1.375 - i*2.3815

Approved by eNotes Editorial Team

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