What are the solutions to the equation (5-2x)^3=-1 ?

The solutions to the equation (5-2x)^3=-1 are x=3,x= 9/4+i(sqrt(3))/4 ,x= 9/4-i(sqrt(3))/4

Find the zeros of (5-2x)^3=-1

The zeros of (5-2x)^3=-1 are x=3,x= 9/4+i(sqrt(3))/4 ,x= 9/4-i(sqrt(3))/4

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(5 - 2 x)^{3} = - 1

x = 3, x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

Solution steps

(5 - 2 x)^{3} = - 1

Expand

(5 - 2 x)^{3} : 125 - 150 x + 60 x^{2} - 8 x^{3}

125 - 150 x + 60 x^{2} - 8 x^{3} = - 1

Move

1

to the left side

- 8 x^{3} + 60 x^{2} - 150 x + 126 = 0

Factor

- 8 x^{3} + 60 x^{2} - 150 x + 126 : - 2 (x - 3) (4 x^{2} - 18 x + 21)

- 2 (x - 3) (4 x^{2} - 18 x + 21) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 4 x^{2} - 18 x + 21 = 0

Solve

x - 3 = 0 : x = 3

Solve

4 x^{2} - 18 x + 21 = 0 : x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

The solutions are

x = 3, x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

x^{3} + 10 x^{2} + 16 x = 0

x^{4} + x^{3} - 8 x^{2} - 9 x - 9 = 0

(x - 3) (x - 1)^{2} (x^{2} + 4 x + 13) = 0

- 2 x^{3} + x^{2} + 13 x + 6 = 0

x x^{2} = 4

What are the solutions to the equation (5-2x)^3=-1 ?
The solutions to the equation (5-2x)^3=-1 are x=3,x= 9/4+i(sqrt(3))/4 ,x= 9/4-i(sqrt(3))/4
Find the zeros of (5-2x)^3=-1
The zeros of (5-2x)^3=-1 are x=3,x= 9/4+i(sqrt(3))/4 ,x= 9/4-i(sqrt(3))/4