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

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

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

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

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(x - 1) \cdot x^{2} = 2 \cdot 3^{2}

x = 3, x = - 1 + 5 i, x = - 1 - 5 i

Solution steps

(x - 1) x^{2} = 2 \cdot 3^{2}

Expand

(x - 1) x^{2} : x^{3} - x^{2}

Expand

2 \cdot 3^{2} : 18

x^{3} - x^{2} = 18

Move

18

to the left side

x^{3} - x^{2} - 18 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 2 x + 6 = 0 : x = - 1 + 5 i, x = - 1 - 5 i

The solutions are

x = 3, x = - 1 + 5 i, x = - 1 - 5 i

x^{3} - 8 x^{2} + 17 x - 30 = 0

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

(y^{2} - 7)^{2} + 7 (y^{2} - 7) - 18 = 0

k^{3} = 343

2 x^{3} + 72 = 200

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