What are the solutions to the equation w^7+2(4w-9)=-3(3w-1)+9w ?

The solutions to the equation w^7+2(4w-9)=-3(3w-1)+9w are w\approx 1.38750…

Find the zeros of w^7+2(4w-9)=-3(3w-1)+9w

The zeros of w^7+2(4w-9)=-3(3w-1)+9w are w\approx 1.38750…

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w^{7} + 2 (4 w - 9) = - 3 (3 w - 1) + 9 w

w \approx 1.38750 \dots

Solution steps

w^{7} + 2 (4 w - 9) = - 3 (3 w - 1) + 9 w

Expand

w^{7} + 2 (4 w - 9) : w^{7} + 8 w - 18

Expand

- 3 (3 w - 1) + 9 w : 3

w^{7} + 8 w - 18 = 3

Move

3

to the left side

w^{7} + 8 w - 21 = 0

Find one solution for

w^{7} + 8 w - 21 = 0

using Newton-Raphson:

w \approx 1.38750 \dots

Apply long division:

\frac{w ^{7} + 8 w - 21}{w - 1.38750 \dots} = w^{6} + 1.38750 \dots w^{5} + 1.92516 \dots w^{4} + 2.67116 \dots w^{3} + 3.70624 \dots w^{2} + 5.14242 \dots w + 15.13511 \dots

w^{6} + 1.38750 \dots w^{5} + 1.92516 \dots w^{4} + 2.67116 \dots w^{3} + 3.70624 \dots w^{2} + 5.14242 \dots w + 15.13511 \dots \approx 0

Find one solution for

w^{6} + 1.38750 \dots w^{5} + 1.92516 \dots w^{4} + 2.67116 \dots w^{3} + 3.70624 \dots w^{2} + 5.14242 \dots w + 15.13511 \dots = 0

using Newton-Raphson:

No Solution for

w \in R

The solution is

w \approx 1.38750 \dots

x^{3} - 4 x = 3 x + 6

(p^{2} - 3)^{2} - 7 (p^{2} - 3) + 6 = 0

25 x^{2} (5 x - 8) - 16 (5 x - 8) = 0

1200 = 360 (1 + x)^{10}

60 \cdot m^{5} = 45

What are the solutions to the equation w^7+2(4w-9)=-3(3w-1)+9w ?
The solutions to the equation w^7+2(4w-9)=-3(3w-1)+9w are w\approx 1.38750…
Find the zeros of w^7+2(4w-9)=-3(3w-1)+9w
The zeros of w^7+2(4w-9)=-3(3w-1)+9w are w\approx 1.38750…