What are the solutions to the equation 12-2x=x^2-4x^9 ?

The solutions to the equation 12-2x=x^2-4x^9 are x\approx-1.13973…

Find the zeros of 12-2x=x^2-4x^9

The zeros of 12-2x=x^2-4x^9 are x\approx-1.13973…

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12 - 2 x = x^{2} - 4 x^{9}

x \approx - 1.13973 \dots

Solution steps

12 - 2 x = x^{2} - 4 x^{9}

Switch sides

x^{2} - 4 x^{9} = 12 - 2 x

Move

2 x

to the left side

x^{2} - 4 x^{9} + 2 x = 12

Move

12

to the left side

x^{2} - 4 x^{9} + 2 x - 12 = 0

Write in the standard form

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

- 4 x^{9} + x^{2} + 2 x - 12 = 0

Find one solution for

- 4 x^{9} + x^{2} + 2 x - 12 = 0

using Newton-Raphson:

x \approx - 1.13973 \dots

Apply long division:

\frac{- 4 x ^{9} + x ^{2} + 2 x - 12}{x + 1.13973 \dots} = - 4 x^{8} + 4.55893 \dots x^{7} - 5.19597 \dots x^{6} + 5.92202 \dots x^{5} - 6.74953 \dots x^{4} + 7.69266 \dots x^{3} - 8.76759 \dots x^{2} + 10.99272 \dots x - 10.52877 \dots

- 4 x^{8} + 4.55893 \dots x^{7} - 5.19597 \dots x^{6} + 5.92202 \dots x^{5} - 6.74953 \dots x^{4} + 7.69266 \dots x^{3} - 8.76759 \dots x^{2} + 10.99272 \dots x - 10.52877 \dots \approx 0

Find one solution for

- 4 x^{8} + 4.55893 \dots x^{7} - 5.19597 \dots x^{6} + 5.92202 \dots x^{5} - 6.74953 \dots x^{4} + 7.69266 \dots x^{3} - 8.76759 \dots x^{2} + 10.99272 \dots x - 10.52877 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.13973 \dots

- x^{5} + 4 x^{4} - x^{3} + 4 x^{2} = 0

x^{4} + 2 x^{2} = 8

x^{3} - 11 x^{2} + 30 x = 0

x^{6} + 4 x^{3} + 16 = 0

(x - 7) (x^{2} - 36) = 0

What are the solutions to the equation 12-2x=x^2-4x^9 ?
The solutions to the equation 12-2x=x^2-4x^9 are x\approx-1.13973…
Find the zeros of 12-2x=x^2-4x^9
The zeros of 12-2x=x^2-4x^9 are x\approx-1.13973…