What are the solutions to the equation 2n+28=n^3 ?

The solutions to the equation 2n+28=n^3 are n\approx 3.25577…

Find the zeros of 2n+28=n^3

The zeros of 2n+28=n^3 are n\approx 3.25577…

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2 n + 28 = n^{3}

n \approx 3.25577 \dots

Solution steps

2 n + 28 = n^{3}

Switch sides

n^{3} = 2 n + 28

Move

28

to the left side

n^{3} - 28 = 2 n

Move

2 n

to the left side

n^{3} - 28 - 2 n = 0

Write in the standard form

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

n^{3} - 2 n - 28 = 0

Find one solution for

n^{3} - 2 n - 28 = 0

using Newton-Raphson:

n \approx 3.25577 \dots

Apply long division:

\frac{n ^{3} - 2 n - 28}{n - 3.25577 \dots} = n^{2} + 3.25577 \dots n + 8.60009 \dots

n^{2} + 3.25577 \dots n + 8.60009 \dots \approx 0

Find one solution for

n^{2} + 3.25577 \dots n + 8.60009 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solution is

n \approx 3.25577 \dots

7 x^{4} - 42 x^{2} = 35 x

5 x^{4} - 20 x^{3} = 0

y, y^{3} = x^{3} - x

- 4 x^{3} - 24 x^{2} - 72 x - 80 = 0

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

What are the solutions to the equation 2n+28=n^3 ?
The solutions to the equation 2n+28=n^3 are n\approx 3.25577…
Find the zeros of 2n+28=n^3
The zeros of 2n+28=n^3 are n\approx 3.25577…