What are the solutions to the equation -2x^4+7=2x+5 ?

The solutions to the equation -2x^4+7=2x+5 are x\approx 0.72449…,x\approx-1.22074…

Find the zeros of -2x^4+7=2x+5

The zeros of -2x^4+7=2x+5 are x\approx 0.72449…,x\approx-1.22074…

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- 2 x^{4} + 7 = 2 x + 5

x \approx 0.72449 \dots, x \approx - 1.22074 \dots

Solution steps

- 2 x^{4} + 7 = 2 x + 5

Move

5

to the left side

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

Move

2 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.72449 \dots

Apply long division:

\frac{- 2 x ^{4} - 2 x + 2}{x - 0.72449 \dots} = - 2 x^{3} - 1.44898 \dots x^{2} - 1.04977 \dots x - 2.76055 \dots

- 2 x^{3} - 1.44898 \dots x^{2} - 1.04977 \dots x - 2.76055 \dots \approx 0

Find one solution for

- 2 x^{3} - 1.44898 \dots x^{2} - 1.04977 \dots x - 2.76055 \dots = 0

using Newton-Raphson:

x \approx - 1.22074 \dots

Apply long division:

\frac{- 2 x ^{3} - 1.44898 \dots x ^{2} - 1.04977 \dots x - 2.76055 \dots}{x + 1.22074 \dots} = - 2 x^{2} + 0.99250 \dots x - 2.26137 \dots

- 2 x^{2} + 0.99250 \dots x - 2.26137 \dots \approx 0

Find one solution for

- 2 x^{2} + 0.99250 \dots x - 2.26137 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.72449 \dots, x \approx - 1.22074 \dots

(x + 1) (2 x - 1)^{2} = 1

x^{3} + 16 x = 0

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

2 x^{4} - 72 x^{2} = 0

D^{3} - 6 D^{2} + 11 D - 6 = 0

What are the solutions to the equation -2x^4+7=2x+5 ?
The solutions to the equation -2x^4+7=2x+5 are x\approx 0.72449…,x\approx-1.22074…
Find the zeros of -2x^4+7=2x+5
The zeros of -2x^4+7=2x+5 are x\approx 0.72449…,x\approx-1.22074…