What are the solutions to the equation -2x^4+5=3x-2 ?

The solutions to the equation -2x^4+5=3x-2 are x\approx 1.15341…,x\approx-1.55393…

Find the zeros of -2x^4+5=3x-2

The zeros of -2x^4+5=3x-2 are x\approx 1.15341…,x\approx-1.55393…

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- 2 x^{4} + 5 = 3 x - 2

x \approx 1.15341 \dots, x \approx - 1.55393 \dots

Solution steps

- 2 x^{4} + 5 = 3 x - 2

Move

2

to the left side

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

Move

3 x

to the left side

- 2 x^{4} + 7 - 3 x = 0

Write in the standard form

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

- 2 x^{4} - 3 x + 7 = 0

Find one solution for

- 2 x^{4} - 3 x + 7 = 0

using Newton-Raphson:

x \approx 1.15341 \dots

Apply long division:

\frac{- 2 x ^{4} - 3 x + 7}{x - 1.15341 \dots} = - 2 x^{3} - 2.30683 \dots x^{2} - 2.66073 \dots x - 6.06893 \dots

- 2 x^{3} - 2.30683 \dots x^{2} - 2.66073 \dots x - 6.06893 \dots \approx 0

Find one solution for

- 2 x^{3} - 2.30683 \dots x^{2} - 2.66073 \dots x - 6.06893 \dots = 0

using Newton-Raphson:

x \approx - 1.55393 \dots

Apply long division:

\frac{- 2 x ^{3} - 2.30683 \dots x ^{2} - 2.66073 \dots x - 6.06893 \dots}{x + 1.55393 \dots} = - 2 x^{2} + 0.80104 \dots x - 3.90551 \dots

- 2 x^{2} + 0.80104 \dots x - 3.90551 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.80104 \dots x - 3.90551 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.15341 \dots, x \approx - 1.55393 \dots

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

0 = 4 x^{3} - 4 x

x^{3} - 6 x^{2} - 5 x + 30 = 0

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

2 r^{4} + 5 r^{3} + r^{2} - 2 r = 0

What are the solutions to the equation -2x^4+5=3x-2 ?
The solutions to the equation -2x^4+5=3x-2 are x\approx 1.15341…,x\approx-1.55393…
Find the zeros of -2x^4+5=3x-2
The zeros of -2x^4+5=3x-2 are x\approx 1.15341…,x\approx-1.55393…