What are the solutions to the equation x-2x^2=1+x^5 ?

The solutions to the equation x-2x^2=1+x^5 are x\approx-1.46557…

Find the zeros of x-2x^2=1+x^5

The zeros of x-2x^2=1+x^5 are x\approx-1.46557…

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x - 2 x^{2} = 1 + x^{5}

x \approx - 1.46557 \dots

Solution steps

x - 2 x^{2} = 1 + x^{5}

Switch sides

1 + x^{5} = x - 2 x^{2}

Move

2 x^{2}

to the left side

1 + x^{5} + 2 x^{2} = x

Move

x

to the left side

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

Write in the standard form

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

x^{5} + 2 x^{2} - x + 1 = 0

Find one solution for

x^{5} + 2 x^{2} - x + 1 = 0

using Newton-Raphson:

x \approx - 1.46557 \dots

Apply long division:

\frac{x ^{5} + 2 x ^{2} - x + 1}{x + 1.46557 \dots} = x^{4} - 1.46557 \dots x^{3} + 2.14789 \dots x^{2} - 1.14789 \dots x + 0.68232 \dots

x^{4} - 1.46557 \dots x^{3} + 2.14789 \dots x^{2} - 1.14789 \dots x + 0.68232 \dots \approx 0

Find one solution for

x^{4} - 1.46557 \dots x^{3} + 2.14789 \dots x^{2} - 1.14789 \dots x + 0.68232 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.46557 \dots

x, x^{4} - 6 x^{2} + 5 = 0

3 (36 x^{2} - 49) (x^{2} + 64) = 0

2 x^{3} = 50 x

30 x^{4} - x^{2} - 1 = 0

m^{3} = 27

What are the solutions to the equation x-2x^2=1+x^5 ?
The solutions to the equation x-2x^2=1+x^5 are x\approx-1.46557…
Find the zeros of x-2x^2=1+x^5
The zeros of x-2x^2=1+x^5 are x\approx-1.46557…