What are the solutions to the equation 8x-2x^3-1=0 ?

The solutions to the equation 8x-2x^3-1=0 are x\approx 0.12549…,x\approx 1.93429…,x\approx-2.05979…

Find the zeros of 8x-2x^3-1=0

The zeros of 8x-2x^3-1=0 are x\approx 0.12549…,x\approx 1.93429…,x\approx-2.05979…

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8 x - 2 x^{3} - 1 = 0

x \approx 0.12549 \dots, x \approx 1.93429 \dots, x \approx - 2.05979 \dots

Solution steps

8 x - 2 x^{3} - 1 = 0

Write in the standard form

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

- 2 x^{3} + 8 x - 1 = 0

Find one solution for

- 2 x^{3} + 8 x - 1 = 0

using Newton-Raphson:

x \approx 0.12549 \dots

Apply long division:

\frac{- 2 x ^{3} + 8 x - 1}{x - 0.12549 \dots} = - 2 x^{2} - 0.25098 \dots x + 7.96850 \dots

- 2 x^{2} - 0.25098 \dots x + 7.96850 \dots \approx 0

Find one solution for

- 2 x^{2} - 0.25098 \dots x + 7.96850 \dots = 0

using Newton-Raphson:

x \approx 1.93429 \dots

Apply long division:

\frac{- 2 x ^{2} - 0.25098 \dots x + 7.96850 \dots}{x - 1.93429 \dots} = - 2 x - 4.11958 \dots

- 2 x - 4.11958 \dots \approx 0

x \approx - 2.05979 \dots

The solutions are

x \approx 0.12549 \dots, x \approx 1.93429 \dots, x \approx - 2.05979 \dots

2 (x + 7) (25 x^{2} - 49) = 0

x^{9} + 3 x^{6} + 3 x^{3} - 16 x - 7 = 0

x^{3} - 3 x^{2} - 9 x + 11 = 0

x x^{2} + 6 x + 8 = 0

x^{3} - 28 = 100

What are the solutions to the equation 8x-2x^3-1=0 ?
The solutions to the equation 8x-2x^3-1=0 are x\approx 0.12549…,x\approx 1.93429…,x\approx-2.05979…
Find the zeros of 8x-2x^3-1=0
The zeros of 8x-2x^3-1=0 are x\approx 0.12549…,x\approx 1.93429…,x\approx-2.05979…