What are the solutions to the equation n^4(n+5)-2(5+7n)=-70 ?

The solutions to the equation n^4(n+5)-2(5+7n)=-70 are n\approx-5.18361…

Find the zeros of n^4(n+5)-2(5+7n)=-70

The zeros of n^4(n+5)-2(5+7n)=-70 are n\approx-5.18361…

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n^{4} (n + 5) - 2 (5 + 7 n) = - 70

n \approx - 5.18361 \dots

Solution steps

n^{4} (n + 5) - 2 (5 + 7 n) = - 70

Expand

n^{4} (n + 5) - 2 (5 + 7 n) : n^{5} + 5 n^{4} - 10 - 14 n

n^{5} + 5 n^{4} - 10 - 14 n = - 70

Move

70

to the left side

n^{5} + 5 n^{4} - 14 n + 60 = 0

Find one solution for

n^{5} + 5 n^{4} - 14 n + 60 = 0

using Newton-Raphson:

n \approx - 5.18361 \dots

Apply long division:

\frac{n ^{5} + 5 n ^{4} - 14 n + 60}{n + 5.18361 \dots} = n^{4} - 0.18361 \dots n^{3} + 0.95180 \dots n^{2} - 4.93379 \dots n + 11.57492 \dots

n^{4} - 0.18361 \dots n^{3} + 0.95180 \dots n^{2} - 4.93379 \dots n + 11.57492 \dots \approx 0

Find one solution for

n^{4} - 0.18361 \dots n^{3} + 0.95180 \dots n^{2} - 4.93379 \dots n + 11.57492 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solution is

n \approx - 5.18361 \dots

z^{4} = 6 z^{2} + 7

7 z^{3} + 30 z^{2} = 25 z

s^{3} + 9.5 s^{2} - 5 s = 0

1 - k^{4} = 0.4583

0 = 2 x^{3} + x^{2} - 5 x + 2

What are the solutions to the equation n^4(n+5)-2(5+7n)=-70 ?
The solutions to the equation n^4(n+5)-2(5+7n)=-70 are n\approx-5.18361…
Find the zeros of n^4(n+5)-2(5+7n)=-70
The zeros of n^4(n+5)-2(5+7n)=-70 are n\approx-5.18361…