What are the solutions to the equation 1/2 (x-6)^3+4=0 ?

The solutions to the equation 1/2 (x-6)^3+4=0 are x=4,x=7+sqrt(3)i,x=7-sqrt(3)i

Find the zeros of 1/2 (x-6)^3+4=0

The zeros of 1/2 (x-6)^3+4=0 are x=4,x=7+sqrt(3)i,x=7-sqrt(3)i

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\frac{1}{2} (x - 6)^{3} + 4 = 0

x = 4, x = 7 + 3 i, x = 7 - 3 i

Solution steps

\frac{1}{2} (x - 6)^{3} + 4 = 0

Multiply both sides by

2

(x - 6)^{3} + 8 = 0

Expand

(x - 6)^{3} + 8 : x^{3} - 18 x^{2} + 108 x - 208

x^{3} - 18 x^{2} + 108 x - 208 = 0

Factor

x^{3} - 18 x^{2} + 108 x - 208 : (x - 4) (x^{2} - 14 x + 52)

(x - 4) (x^{2} - 14 x + 52) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} - 14 x + 52 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} - 14 x + 52 = 0 : x = 7 + 3 i, x = 7 - 3 i

The solutions are

x = 4, x = 7 + 3 i, x = 7 - 3 i

z^{4} - z^{2} = - 1

a, 2 b + a^{3} = b^{1}

15 x^{4} - 50 x + 60 = 0

x + x^{4} = 0

- x^{3} + 12 \cdot x + 16 = 0

What are the solutions to the equation 1/2 (x-6)^3+4=0 ?
The solutions to the equation 1/2 (x-6)^3+4=0 are x=4,x=7+sqrt(3)i,x=7-sqrt(3)i
Find the zeros of 1/2 (x-6)^3+4=0
The zeros of 1/2 (x-6)^3+4=0 are x=4,x=7+sqrt(3)i,x=7-sqrt(3)i