What are the solutions to the equation -2x^4+9=3x-2 ?

The solutions to the equation -2x^4+9=3x-2 are x\approx 1.36336…,x\approx-1.68308…

Find the zeros of -2x^4+9=3x-2

The zeros of -2x^4+9=3x-2 are x\approx 1.36336…,x\approx-1.68308…

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- 2 x^{4} + 9 = 3 x - 2

x \approx 1.36336 \dots, x \approx - 1.68308 \dots

Solution steps

- 2 x^{4} + 9 = 3 x - 2

Move

2

to the left side

- 2 x^{4} + 11 = 3 x

Move

3 x

to the left side

- 2 x^{4} + 11 - 3 x = 0

Write in the standard form

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

- 2 x^{4} - 3 x + 11 = 0

Find one solution for

- 2 x^{4} - 3 x + 11 = 0

using Newton-Raphson:

x \approx 1.36336 \dots

Apply long division:

\frac{- 2 x ^{4} - 3 x + 11}{x - 1.36336 \dots} = - 2 x^{3} - 2.72672 \dots x^{2} - 3.71750 \dots x - 8.06829 \dots

- 2 x^{3} - 2.72672 \dots x^{2} - 3.71750 \dots x - 8.06829 \dots \approx 0

Find one solution for

- 2 x^{3} - 2.72672 \dots x^{2} - 3.71750 \dots x - 8.06829 \dots = 0

using Newton-Raphson:

x \approx - 1.68308 \dots

Apply long division:

\frac{- 2 x ^{3} - 2.72672 \dots x ^{2} - 3.71750 \dots x - 8.06829 \dots}{x + 1.68308 \dots} = - 2 x^{2} + 0.63945 \dots x - 4.79375 \dots

- 2 x^{2} + 0.63945 \dots x - 4.79375 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.63945 \dots x - 4.79375 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.36336 \dots, x \approx - 1.68308 \dots

4 x^{3} - x^{2} + 36 x - 9 = 0

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

x^{4} = 3

x^{4} = 8

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

What are the solutions to the equation -2x^4+9=3x-2 ?
The solutions to the equation -2x^4+9=3x-2 are x\approx 1.36336…,x\approx-1.68308…
Find the zeros of -2x^4+9=3x-2
The zeros of -2x^4+9=3x-2 are x\approx 1.36336…,x\approx-1.68308…