What are the solutions to the equation 10-4w^7=7(w+2)6 ?

The solutions to the equation 10-4w^7=7(w+2)6 are w\approx-1.26586…

Find the zeros of 10-4w^7=7(w+2)6

The zeros of 10-4w^7=7(w+2)6 are w\approx-1.26586…

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10 - 4 w^{7} = 7 (w + 2) 6

w \approx - 1.26586 \dots

Solution steps

10 - 4 w^{7} = 7 (w + 2) \cdot 6

Expand

7 (w + 2) \cdot 6 : 42 w + 84

10 - 4 w^{7} = 42 w + 84

Move

84

to the left side

- 4 w^{7} - 74 = 42 w

Move

42 w

to the left side

- 4 w^{7} - 74 - 42 w = 0

Write in the standard form

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

- 4 w^{7} - 42 w - 74 = 0

Find one solution for

- 4 w^{7} - 42 w - 74 = 0

using Newton-Raphson:

w \approx - 1.26586 \dots

Apply long division:

\frac{- 4 w ^{7} - 42 w - 74}{w + 1.26586 \dots} = - 4 w^{6} + 5.06345 \dots w^{5} - 6.40963 \dots w^{4} + 8.11372 \dots w^{3} - 10.27086 \dots w^{2} + 13.00151 \dots w - 58.45813 \dots

- 4 w^{6} + 5.06345 \dots w^{5} - 6.40963 \dots w^{4} + 8.11372 \dots w^{3} - 10.27086 \dots w^{2} + 13.00151 \dots w - 58.45813 \dots \approx 0

Find one solution for

- 4 w^{6} + 5.06345 \dots w^{5} - 6.40963 \dots w^{4} + 8.11372 \dots w^{3} - 10.27086 \dots w^{2} + 13.00151 \dots w - 58.45813 \dots = 0

using Newton-Raphson:

No Solution for

w \in R

The solution is

w \approx - 1.26586 \dots

x^{3} - x = 2

25 x^{4} - 15 x^{2} + 2 = 0

x^{3} - x = - 1

2 x^{3} - 8 x^{2} - 120 x = 0

7 x^{3} + 11 x^{2} - 13 x + 3 = 0

What are the solutions to the equation 10-4w^7=7(w+2)6 ?
The solutions to the equation 10-4w^7=7(w+2)6 are w\approx-1.26586…
Find the zeros of 10-4w^7=7(w+2)6
The zeros of 10-4w^7=7(w+2)6 are w\approx-1.26586…