What are the solutions to the equation 2x^4+x^3-29x^2-34x=24 ?

The solutions to the equation 2x^4+x^3-29x^2-34x=24 are x\approx-3.52149…,x\approx 4.14957…

Find the zeros of 2x^4+x^3-29x^2-34x=24

The zeros of 2x^4+x^3-29x^2-34x=24 are x\approx-3.52149…,x\approx 4.14957…

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2 x^{4} + x^{3} - 29 x^{2} - 34 x = 24

x \approx - 3.52149 \dots, x \approx 4.14957 \dots

Solution steps

2 x^{4} + x^{3} - 29 x^{2} - 34 x = 24

Move

24

to the left side

2 x^{4} + x^{3} - 29 x^{2} - 34 x - 24 = 0

Find one solution for

2 x^{4} + x^{3} - 29 x^{2} - 34 x - 24 = 0

using Newton-Raphson:

x \approx - 3.52149 \dots

Apply long division:

\frac{2 x ^{4} + x ^{3} - 29 x ^{2} - 34 x - 24}{x + 3.52149 \dots} = 2 x^{3} - 6.04298 \dots x^{2} - 7.71965 \dots x - 6.81528 \dots

2 x^{3} - 6.04298 \dots x^{2} - 7.71965 \dots x - 6.81528 \dots \approx 0

Find one solution for

2 x^{3} - 6.04298 \dots x^{2} - 7.71965 \dots x - 6.81528 \dots = 0

using Newton-Raphson:

x \approx 4.14957 \dots

Apply long division:

\frac{2 x ^{3} - 6.04298 \dots x ^{2} - 7.71965 \dots x - 6.81528 \dots}{x - 4.14957 \dots} = 2 x^{2} + 2.25615 \dots x + 1.64240 \dots

2 x^{2} + 2.25615 \dots x + 1.64240 \dots \approx 0

Find one solution for

2 x^{2} + 2.25615 \dots x + 1.64240 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 3.52149 \dots, x \approx 4.14957 \dots

400 = t^{3} + 2 t

(x^{2} - 3)^{2} = 36

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

x^{4} - x^{3} + 1 = 0

3 x^{3} - 14 x - 5 = 0

What are the solutions to the equation 2x^4+x^3-29x^2-34x=24 ?
The solutions to the equation 2x^4+x^3-29x^2-34x=24 are x\approx-3.52149…,x\approx 4.14957…
Find the zeros of 2x^4+x^3-29x^2-34x=24
The zeros of 2x^4+x^3-29x^2-34x=24 are x\approx-3.52149…,x\approx 4.14957…