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

The solutions to the equation -2x^4+9=2x-3 are x\approx 1.45972…,x\approx-1.66384…

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

The zeros of -2x^4+9=2x-3 are x\approx 1.45972…,x\approx-1.66384…

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

x \approx 1.45972 \dots, x \approx - 1.66384 \dots

Solution steps

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

Move

3

to the left side

- 2 x^{4} + 12 = 2 x

Move

2 x

to the left side

- 2 x^{4} + 12 - 2 x = 0

Write in the standard form

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

- 2 x^{4} - 2 x + 12 = 0

Find one solution for

- 2 x^{4} - 2 x + 12 = 0

using Newton-Raphson:

x \approx 1.45972 \dots

Apply long division:

\frac{- 2 x ^{4} - 2 x + 12}{x - 1.45972 \dots} = - 2 x^{3} - 2.91944 \dots x^{2} - 4.26158 \dots x - 8.22073 \dots

- 2 x^{3} - 2.91944 \dots x^{2} - 4.26158 \dots x - 8.22073 \dots \approx 0

Find one solution for

- 2 x^{3} - 2.91944 \dots x^{2} - 4.26158 \dots x - 8.22073 \dots = 0

using Newton-Raphson:

x \approx - 1.66384 \dots

Apply long division:

\frac{- 2 x ^{3} - 2.91944 \dots x ^{2} - 4.26158 \dots x - 8.22073 \dots}{x + 1.66384 \dots} = - 2 x^{2} + 0.40823 \dots x - 4.94082 \dots

- 2 x^{2} + 0.40823 \dots x - 4.94082 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.40823 \dots x - 4.94082 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.45972 \dots, x \approx - 1.66384 \dots

x^{4} + x^{3} - 4 x^{2} + 2 x - 12 = 0

3 x^{3} - 3 x^{2} - 270 x = 0

a - 2 a^{5} = 3

- x^{3} + 7 x^{2} - 15 x + 9 = 0

x^{10} = 1

What are the solutions to the equation -2x^4+9=2x-3 ?
The solutions to the equation -2x^4+9=2x-3 are x\approx 1.45972…,x\approx-1.66384…
Find the zeros of -2x^4+9=2x-3
The zeros of -2x^4+9=2x-3 are x\approx 1.45972…,x\approx-1.66384…