What are the solutions to the equation x^4+x^3=3-4x ?

The solutions to the equation x^4+x^3=3-4x are x\approx 0.64160…,x\approx-2.15774…

Find the zeros of x^4+x^3=3-4x

The zeros of x^4+x^3=3-4x are x\approx 0.64160…,x\approx-2.15774…

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x^{4} + x^{3} = 3 - 4 x

x \approx 0.64160 \dots, x \approx - 2.15774 \dots

Solution steps

x^{4} + x^{3} = 3 - 4 x

Move

4 x

to the left side

x^{4} + x^{3} + 4 x = 3

Move

3

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.64160 \dots

Apply long division:

\frac{x ^{4} + x ^{3} + 4 x - 3}{x - 0.64160 \dots} = x^{3} + 1.64160 \dots x^{2} + 1.05326 \dots x + 4.67577 \dots

x^{3} + 1.64160 \dots x^{2} + 1.05326 \dots x + 4.67577 \dots \approx 0

Find one solution for

x^{3} + 1.64160 \dots x^{2} + 1.05326 \dots x + 4.67577 \dots = 0

using Newton-Raphson:

x \approx - 2.15774 \dots

Apply long division:

\frac{x ^{3} + 1.64160 \dots x ^{2} + 1.05326 \dots x + 4.67577 \dots}{x + 2.15774 \dots} = x^{2} - 0.51614 \dots x + 2.16697 \dots

x^{2} - 0.51614 \dots x + 2.16697 \dots \approx 0

Find one solution for

x^{2} - 0.51614 \dots x + 2.16697 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.64160 \dots, x \approx - 2.15774 \dots

2 x^{3} - 3 x + 6 = 0

2 x^{3} + 6 x^{2} + 6 x = 0

x, u = x^{3} + y^{3}

y, 9 + y^{3} = - x

(x + 2)^{4} + x^{4} = 82

What are the solutions to the equation x^4+x^3=3-4x ?
The solutions to the equation x^4+x^3=3-4x are x\approx 0.64160…,x\approx-2.15774…
Find the zeros of x^4+x^3=3-4x
The zeros of x^4+x^3=3-4x are x\approx 0.64160…,x\approx-2.15774…