What are the solutions to the equation 3x^3+16^2=12x ?

The solutions to the equation 3x^3+16^2=12x are x\approx-4.70497…

Find the zeros of 3x^3+16^2=12x

The zeros of 3x^3+16^2=12x are x\approx-4.70497…

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3 x^{3} + 1 6^{2} = 12 x

x \approx - 4.70497 \dots

Solution steps

3 x^{3} + 1 6^{2} = 12 x

Expand

3 x^{3} + 1 6^{2} : 3 x^{3} + 256

3 x^{3} + 256 = 12 x

Move

12 x

to the left side

3 x^{3} + 256 - 12 x = 0

Write in the standard form

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

3 x^{3} - 12 x + 256 = 0

Find one solution for

3 x^{3} - 12 x + 256 = 0

using Newton-Raphson:

x \approx - 4.70497 \dots

Apply long division:

\frac{3 x ^{3} - 12 x + 256}{x + 4.70497 \dots} = 3 x^{2} - 14.11493 \dots x + 54.41045 \dots

3 x^{2} - 14.11493 \dots x + 54.41045 \dots \approx 0

Find one solution for

3 x^{2} - 14.11493 \dots x + 54.41045 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 4.70497 \dots

x, 3 x^{4} = 81 x

x^{2} + 1 = 4 x^{4} x

2 - x = x^{4}

4 x^{4} + x^{3} + x^{2} + x + 1 = 0

2 x^{3} + 3 x^{2} - 32 x + 15 = 0

What are the solutions to the equation 3x^3+16^2=12x ?
The solutions to the equation 3x^3+16^2=12x are x\approx-4.70497…
Find the zeros of 3x^3+16^2=12x
The zeros of 3x^3+16^2=12x are x\approx-4.70497…