What are the solutions to the equation (x-2)^3=25(x-2) ?

The solutions to the equation (x-2)^3=25(x-2) are x=2,x=-3,x=7

Find the zeros of (x-2)^3=25(x-2)

The zeros of (x-2)^3=25(x-2) are x=2,x=-3,x=7

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(x - 2)^{3} = 25 (x - 2)

x = 2, x = - 3, x = 7

Solution steps

(x - 2)^{3} = 25 (x - 2)

Expand

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

Expand

25 (x - 2) : 25 x - 50

x^{3} - 6 x^{2} + 12 x - 8 = 25 x - 50

Move

50

to the left side

x^{3} - 6 x^{2} + 12 x + 42 = 25 x

Move

25 x

to the left side

x^{3} - 6 x^{2} - 13 x + 42 = 0

Factor

x^{3} - 6 x^{2} - 13 x + 42 : (x - 2) (x + 3) (x - 7)

(x - 2) (x + 3) (x - 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x + 3 = 0 or x - 7 = 0

Solve

x - 2 = 0 : x = 2

Solve

x + 3 = 0 : x = - 3

Solve

x - 7 = 0 : x = 7

The solutions are

x = 2, x = - 3, x = 7

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

- x^{3} + 12 x^{2} - 21 x - 98 = 0

x^{3} - x^{2} = 4

5 x^{3} + 6 x^{2} - 18 x + 5 = 0

x^{4} - 2 x^{2} - 24 = 0

What are the solutions to the equation (x-2)^3=25(x-2) ?
The solutions to the equation (x-2)^3=25(x-2) are x=2,x=-3,x=7
Find the zeros of (x-2)^3=25(x-2)
The zeros of (x-2)^3=25(x-2) are x=2,x=-3,x=7