What are the solutions to the equation -2x^4+7=3x+1 ?

The solutions to the equation -2x^4+7=3x+1 are x\approx 1.08297…,x\approx-1.51535…

Find the zeros of -2x^4+7=3x+1

The zeros of -2x^4+7=3x+1 are x\approx 1.08297…,x\approx-1.51535…

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- 2 x^{4} + 7 = 3 x + 1

x \approx 1.08297 \dots, x \approx - 1.51535 \dots

Solution steps

- 2 x^{4} + 7 = 3 x + 1

Move

1

to the left side

- 2 x^{4} + 6 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.08297 \dots

Apply long division:

\frac{- 2 x ^{4} - 3 x + 6}{x - 1.08297 \dots} = - 2 x^{3} - 2.16594 \dots x^{2} - 2.34566 \dots x - 5.54029 \dots

- 2 x^{3} - 2.16594 \dots x^{2} - 2.34566 \dots x - 5.54029 \dots \approx 0

Find one solution for

- 2 x^{3} - 2.16594 \dots x^{2} - 2.34566 \dots x - 5.54029 \dots = 0

using Newton-Raphson:

x \approx - 1.51535 \dots

Apply long division:

\frac{- 2 x ^{3} - 2.16594 \dots x ^{2} - 2.34566 \dots x - 5.54029 \dots}{x + 1.51535 \dots} = - 2 x^{2} + 0.86476 \dots x - 3.65609 \dots

- 2 x^{2} + 0.86476 \dots x - 3.65609 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.86476 \dots x - 3.65609 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.08297 \dots, x \approx - 1.51535 \dots

3 x^{3} - 27 x^{2} = 0

x, 135 = 5 x^{3}

y, x = (y - 2)^{3} + 1

y, x = (y - 2)^{3} + 2

24 = x (x^{2} - 12 x + 48)

What are the solutions to the equation -2x^4+7=3x+1 ?
The solutions to the equation -2x^4+7=3x+1 are x\approx 1.08297…,x\approx-1.51535…
Find the zeros of -2x^4+7=3x+1
The zeros of -2x^4+7=3x+1 are x\approx 1.08297…,x\approx-1.51535…