What are the solutions to the equation 2x^3-3x^2=6x-9 ?

The solutions to the equation 2x^3-3x^2=6x-9 are x= 3/2 ,x=-sqrt(3),x=sqrt(3)

Find the zeros of 2x^3-3x^2=6x-9

The zeros of 2x^3-3x^2=6x-9 are x= 3/2 ,x=-sqrt(3),x=sqrt(3)

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2 x^{3} - 3 x^{2} = 6 x - 9

x = \frac{3}{2}, x = - 3, x = 3

Decimal Notation

x = 1.5, x = - 1.73205 \dots, x = 1.73205 \dots

Solution steps

2 x^{3} - 3 x^{2} = 6 x - 9

Move

9

to the left side

2 x^{3} - 3 x^{2} + 9 = 6 x

Move

6 x

to the left side

2 x^{3} - 3 x^{2} + 9 - 6 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

2 x^{3} - 3 x^{2} - 6 x + 9 = 0

Factor

2 x^{3} - 3 x^{2} - 6 x + 9 : (2 x - 3) (x + 3) (x - 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 x - 3 = 0 : x = \frac{3}{2}

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

x = \frac{3}{2}, x = - 3, x = 3

x^{3} - 1000 = 0

x^{2} (x - 5) = 0

x^{8} - 17 x^{4} + 16 = 0

x^{3} + 8 i = 0

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

What are the solutions to the equation 2x^3-3x^2=6x-9 ?
The solutions to the equation 2x^3-3x^2=6x-9 are x= 3/2 ,x=-sqrt(3),x=sqrt(3)
Find the zeros of 2x^3-3x^2=6x-9
The zeros of 2x^3-3x^2=6x-9 are x= 3/2 ,x=-sqrt(3),x=sqrt(3)