What are the solutions to the equation -7x-(x+6)=9+2x^9+2x ?

The solutions to the equation -7x-(x+6)=9+2x^9+2x are x\approx-1.08460…

Find the zeros of -7x-(x+6)=9+2x^9+2x

The zeros of -7x-(x+6)=9+2x^9+2x are x\approx-1.08460…

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- 7 x - (x + 6) = 9 + 2 x^{9} + 2 x

x \approx - 1.08460 \dots

Solution steps

- 7 x - (x + 6) = 9 + 2 x^{9} + 2 x

Expand

- 7 x - (x + 6) : - 8 x - 6

- 8 x - 6 = 9 + 2 x^{9} + 2 x

Switch sides

9 + 2 x^{9} + 2 x = - 8 x - 6

Move

6

to the left side

2 x^{9} + 2 x + 15 = - 8 x

Move

8 x

to the left side

2 x^{9} + 10 x + 15 = 0

Find one solution for

2 x^{9} + 10 x + 15 = 0

using Newton-Raphson:

x \approx - 1.08460 \dots

Apply long division:

\frac{2 x ^{9} + 10 x + 15}{x + 1.08460 \dots} = 2 x^{8} - 2.16920 \dots x^{7} + 2.35272 \dots x^{6} - 2.55176 \dots x^{5} + 2.76765 \dots x^{4} - 3.00180 \dots x^{3} + 3.25576 \dots x^{2} - 3.53120 \dots x + 13.82995 \dots

2 x^{8} - 2.16920 \dots x^{7} + 2.35272 \dots x^{6} - 2.55176 \dots x^{5} + 2.76765 \dots x^{4} - 3.00180 \dots x^{3} + 3.25576 \dots x^{2} - 3.53120 \dots x + 13.82995 \dots \approx 0

Find one solution for

2 x^{8} - 2.16920 \dots x^{7} + 2.35272 \dots x^{6} - 2.55176 \dots x^{5} + 2.76765 \dots x^{4} - 3.00180 \dots x^{3} + 3.25576 \dots x^{2} - 3.53120 \dots x + 13.82995 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.08460 \dots

x^{7} - 64 x = 0

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

x^{3} - 16 x^{2} + 63 x = 0

a^{3} + a^{2} = 36

- 3 x (2 x - 1) (x + 6)^{2} = 0

What are the solutions to the equation -7x-(x+6)=9+2x^9+2x ?
The solutions to the equation -7x-(x+6)=9+2x^9+2x are x\approx-1.08460…
Find the zeros of -7x-(x+6)=9+2x^9+2x
The zeros of -7x-(x+6)=9+2x^9+2x are x\approx-1.08460…