What are the solutions to the equation 18x^3+9x^2-2x-1=0 ?

The solutions to the equation 18x^3+9x^2-2x-1=0 are x=-1/2 ,x=-1/3 ,x= 1/3

Find the zeros of 18x^3+9x^2-2x-1=0

The zeros of 18x^3+9x^2-2x-1=0 are x=-1/2 ,x=-1/3 ,x= 1/3

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18 x^{3} + 9 x^{2} - 2 x - 1 = 0

x = - \frac{1}{2}, x = - \frac{1}{3}, x = \frac{1}{3}

Decimal Notation

x = - 0.5, x = - 0.33333 \dots, x = 0.33333 \dots

Solution steps

18 x^{3} + 9 x^{2} - 2 x - 1 = 0

Factor

18 x^{3} + 9 x^{2} - 2 x - 1 : (2 x + 1) (3 x + 1) (3 x - 1)

(2 x + 1) (3 x + 1) (3 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or 3 x + 1 = 0 or 3 x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

3 x - 1 = 0 : x = \frac{1}{3}

The solutions are

x = - \frac{1}{2}, x = - \frac{1}{3}, x = \frac{1}{3}

4 x^{3} - 1 = 2 x^{2} - 2 x

x^{3} + 4 x - 4 = 0

x (x + 4) (x - 1) = 0

x^{3} - 49 x + 120 = 0

- x^{3} + 12 x^{2} - 21 x + 10 = 0

What are the solutions to the equation 18x^3+9x^2-2x-1=0 ?
The solutions to the equation 18x^3+9x^2-2x-1=0 are x=-1/2 ,x=-1/3 ,x= 1/3
Find the zeros of 18x^3+9x^2-2x-1=0
The zeros of 18x^3+9x^2-2x-1=0 are x=-1/2 ,x=-1/3 ,x= 1/3