What are the solutions to the equation 27x^3+36x=8+54x^2 ?

The solutions to the equation 27x^3+36x=8+54x^2 are x= 2/3

Find the zeros of 27x^3+36x=8+54x^2

The zeros of 27x^3+36x=8+54x^2 are x= 2/3

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27 x^{3} + 36 x = 8 + 54 x^{2}

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

27 x^{3} + 36 x = 8 + 54 x^{2}

Move

54 x^{2}

to the left side

27 x^{3} + 36 x - 54 x^{2} = 8

Move

8

to the left side

27 x^{3} + 36 x - 54 x^{2} - 8 = 0

Write in the standard form

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

27 x^{3} - 54 x^{2} + 36 x - 8 = 0

Factor

27 x^{3} - 54 x^{2} + 36 x - 8 : (3 x - 2)^{3}

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x - 2 = 0

Solve

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

The solution is

x = \frac{2}{3}

729 = x^{3}

z, z^{6} + 4 z^{3} + 16 = 0

(2 - j) z^{4} + 1 - 2 j = 0

343 = x^{3}

n^{2} = n^{3} + n^{1}

What are the solutions to the equation 27x^3+36x=8+54x^2 ?
The solutions to the equation 27x^3+36x=8+54x^2 are x= 2/3
Find the zeros of 27x^3+36x=8+54x^2
The zeros of 27x^3+36x=8+54x^2 are x= 2/3