What are the solutions to the equation -2x^4+9=2x+1 ?

The solutions to the equation -2x^4+9=2x+1 are x\approx 1.28378…,x\approx-1.53375…

Find the zeros of -2x^4+9=2x+1

The zeros of -2x^4+9=2x+1 are x\approx 1.28378…,x\approx-1.53375…

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- 2 x^{4} + 9 = 2 x + 1

x \approx 1.28378 \dots, x \approx - 1.53375 \dots

Solution steps

- 2 x^{4} + 9 = 2 x + 1

Move

1

to the left side

- 2 x^{4} + 8 = 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.28378 \dots

Apply long division:

\frac{- 2 x ^{4} - 2 x + 8}{x - 1.28378 \dots} = - 2 x^{3} - 2.56756 \dots x^{2} - 3.29619 \dots x - 6.23158 \dots

- 2 x^{3} - 2.56756 \dots x^{2} - 3.29619 \dots x - 6.23158 \dots \approx 0

Find one solution for

- 2 x^{3} - 2.56756 \dots x^{2} - 3.29619 \dots x - 6.23158 \dots = 0

using Newton-Raphson:

x \approx - 1.53375 \dots

Apply long division:

\frac{- 2 x ^{3} - 2.56756 \dots x ^{2} - 3.29619 \dots x - 6.23158 \dots}{x + 1.53375 \dots} = - 2 x^{2} + 0.49993 \dots x - 4.06297 \dots

- 2 x^{2} + 0.49993 \dots x - 4.06297 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.49993 \dots x - 4.06297 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.28378 \dots, x \approx - 1.53375 \dots

39 = p^{3} + 32

x^{3} + x^{2} + 17 x - 15 = 0

(x + 4)^{3} - 72 = 0

x^{3} + 7.8 x^{2} - 0.0844 = 0

x^{4} + 4 x^{3} - 8 x = 0

What are the solutions to the equation -2x^4+9=2x+1 ?
The solutions to the equation -2x^4+9=2x+1 are x\approx 1.28378…,x\approx-1.53375…
Find the zeros of -2x^4+9=2x+1
The zeros of -2x^4+9=2x+1 are x\approx 1.28378…,x\approx-1.53375…