What are the solutions to the equation 27x^3+27x^2+9x=-1 ?

The solutions to the equation 27x^3+27x^2+9x=-1 are x=-1/3

Find the zeros of 27x^3+27x^2+9x=-1

The zeros of 27x^3+27x^2+9x=-1 are x=-1/3

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27 x^{3} + 27 x^{2} + 9 x = - 1

x = - \frac{1}{3}

Decimal Notation

x = - 0.33333 \dots

Solution steps

27 x^{3} + 27 x^{2} + 9 x = - 1

Move

1

to the left side

27 x^{3} + 27 x^{2} + 9 x + 1 = 0

Factor

27 x^{3} + 27 x^{2} + 9 x + 1 : (3 x + 1)^{3}

(3 x + 1)^{3} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x + 1 = 0

Solve

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

The solution is

x = - \frac{1}{3}

6 x^{3} + 43 x^{2} + 43 x + 6 = 0

(x^{2} + 8)^{2} - (x^{2} + 8) - 72 = 0

4 x^{4} - 12 x^{2} - 7 = 0

28 x^{3} - 6 x^{2} + 12 x - 8 = 0

100 = \frac{4}{3} π r^{3}

What are the solutions to the equation 27x^3+27x^2+9x=-1 ?
The solutions to the equation 27x^3+27x^2+9x=-1 are x=-1/3
Find the zeros of 27x^3+27x^2+9x=-1
The zeros of 27x^3+27x^2+9x=-1 are x=-1/3