What are the solutions to the equation 2x^3+(1-x^2)^4=0 ?

The solutions to the equation 2x^3+(1-x^2)^4=0 are x\approx-0.52066…,x\approx-1.65349…

Find the zeros of 2x^3+(1-x^2)^4=0

The zeros of 2x^3+(1-x^2)^4=0 are x\approx-0.52066…,x\approx-1.65349…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2 x^{3} + (1 - x^{2})^{4} = 0

x \approx - 0.52066 \dots, x \approx - 1.65349 \dots

Solution steps

2 x^{3} + (1 - x^{2})^{4} = 0

Expand

2 x^{3} + (1 - x^{2})^{4} : 2 x^{3} + 1 - 4 x^{2} + 6 x^{4} - 4 x^{6} + x^{8}

2 x^{3} + 1 - 4 x^{2} + 6 x^{4} - 4 x^{6} + x^{8} = 0

Write in the standard form

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

x^{8} - 4 x^{6} + 6 x^{4} + 2 x^{3} - 4 x^{2} + 1 = 0

Find one solution for

x^{8} - 4 x^{6} + 6 x^{4} + 2 x^{3} - 4 x^{2} + 1 = 0

using Newton-Raphson:

x \approx - 0.52066 \dots

Apply long division:

\frac{x ^{8} - 4 x ^{6} + 6 x ^{4} + 2 x ^{3} - 4 x ^{2} + 1}{x + 0.52066 \dots} = x^{7} - 0.52066 \dots x^{6} - 3.72891 \dots x^{5} + 1.94150 \dots x^{4} + 4.98913 \dots x^{3} - 0.59765 \dots x^{2} - 3.68882 \dots x + 1.92063 \dots

x^{7} - 0.52066 \dots x^{6} - 3.72891 \dots x^{5} + 1.94150 \dots x^{4} + 4.98913 \dots x^{3} - 0.59765 \dots x^{2} - 3.68882 \dots x + 1.92063 \dots \approx 0

Find one solution for

x^{7} - 0.52066 \dots x^{6} - 3.72891 \dots x^{5} + 1.94150 \dots x^{4} + 4.98913 \dots x^{3} - 0.59765 \dots x^{2} - 3.68882 \dots x + 1.92063 \dots = 0

using Newton-Raphson:

x \approx - 1.65349 \dots

Apply long division:

\frac{x ^{7} - 0.52066 \dots x ^{6} - 3.72891 \dots x ^{5} + 1.94150 \dots x ^{4} + 4.98913 \dots x ^{3} - 0.59765 \dots x ^{2} - 3.68882 \dots x + 1.92063 \dots}{x + 1.65349 \dots} = x^{6} - 2.17415 \dots x^{5} - 0.13395 \dots x^{4} + 2.16300 \dots x^{3} + 1.41262 \dots x^{2} - 2.93341 \dots x + 1.16155 \dots

x^{6} - 2.17415 \dots x^{5} - 0.13395 \dots x^{4} + 2.16300 \dots x^{3} + 1.41262 \dots x^{2} - 2.93341 \dots x + 1.16155 \dots \approx 0

Find one solution for

x^{6} - 2.17415 \dots x^{5} - 0.13395 \dots x^{4} + 2.16300 \dots x^{3} + 1.41262 \dots x^{2} - 2.93341 \dots x + 1.16155 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.52066 \dots, x \approx - 1.65349 \dots

3 x^{3} + 4 x^{2} + 27 x + 36 = 0

d x^{3}

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

10 x + 0.5 x^{2} - 0.001 x^{3} - 5000 = 0

x^{4} - x^{2} = 7 x^{2} + 9

What are the solutions to the equation 2x^3+(1-x^2)^4=0 ?
The solutions to the equation 2x^3+(1-x^2)^4=0 are x\approx-0.52066…,x\approx-1.65349…
Find the zeros of 2x^3+(1-x^2)^4=0
The zeros of 2x^3+(1-x^2)^4=0 are x\approx-0.52066…,x\approx-1.65349…