What are the solutions to the equation 8n^{12}(2+2n)=10(-2n-7)+2 ?

The solutions to the equation 8n^{12}(2+2n)=10(-2n-7)+2 are n\approx-1.22885…

Find the zeros of 8n^{12}(2+2n)=10(-2n-7)+2

The zeros of 8n^{12}(2+2n)=10(-2n-7)+2 are n\approx-1.22885…

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8 n^{12} (2 + 2 n) = 10 (- 2 n - 7) + 2

n \approx - 1.22885 \dots

Solution steps

8 n^{12} (2 + 2 n) = 10 (- 2 n - 7) + 2

Expand

8 n^{12} (2 + 2 n) : 16 n^{12} + 16 n^{13}

Expand

10 (- 2 n - 7) + 2 : - 20 n - 68

16 n^{12} + 16 n^{13} = - 20 n - 68

Move

68

to the left side

16 n^{12} + 16 n^{13} + 68 = - 20 n

Move

20 n

to the left side

16 n^{12} + 16 n^{13} + 68 + 20 n = 0

Write in the standard form

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

16 n^{13} + 16 n^{12} + 20 n + 68 = 0

Find one solution for

16 n^{13} + 16 n^{12} + 20 n + 68 = 0

using Newton-Raphson:

n \approx - 1.22885 \dots

Apply long division:

\frac{16 n ^{13} + 16 n ^{12} + 20 n + 68}{n + 1.22885 \dots} = 16 n^{12} - 3.66175 \dots n^{11} + 4.49978 \dots n^{10} - 5.52960 \dots n^{9} + 6.79511 \dots n^{8} - 8.35024 \dots n^{7} + 10.26127 \dots n^{6} - 12.60967 \dots n^{5} + 15.49551 \dots n^{4} - 19.04181 \dots n^{3} + 23.39972 \dots n^{2} - 28.75498 \dots n + 55.33584 \dots

16 n^{12} - 3.66175 \dots n^{11} + 4.49978 \dots n^{10} - 5.52960 \dots n^{9} + 6.79511 \dots n^{8} - 8.35024 \dots n^{7} + 10.26127 \dots n^{6} - 12.60967 \dots n^{5} + 15.49551 \dots n^{4} - 19.04181 \dots n^{3} + 23.39972 \dots n^{2} - 28.75498 \dots n + 55.33584 \dots \approx 0

Find one solution for

16 n^{12} - 3.66175 \dots n^{11} + 4.49978 \dots n^{10} - 5.52960 \dots n^{9} + 6.79511 \dots n^{8} - 8.35024 \dots n^{7} + 10.26127 \dots n^{6} - 12.60967 \dots n^{5} + 15.49551 \dots n^{4} - 19.04181 \dots n^{3} + 23.39972 \dots n^{2} - 28.75498 \dots n + 55.33584 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solution is

n \approx - 1.22885 \dots

c^{3} = 1728

(2 + 4) 6 = 2 x^{6} + 4 x^{6}

3 x^{5} + x - 7 = 0

(x + 3) (x^{2} + 2 x + 6) = - (x + 3) (x - 4)

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

What are the solutions to the equation 8n^{12}(2+2n)=10(-2n-7)+2 ?
The solutions to the equation 8n^{12}(2+2n)=10(-2n-7)+2 are n\approx-1.22885…
Find the zeros of 8n^{12}(2+2n)=10(-2n-7)+2
The zeros of 8n^{12}(2+2n)=10(-2n-7)+2 are n\approx-1.22885…