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

The solutions to the equation -2x^4+7=3x+4 are x\approx 0.76803…,x\approx-1.37365…

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

The zeros of -2x^4+7=3x+4 are x\approx 0.76803…,x\approx-1.37365…

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

x \approx 0.76803 \dots, x \approx - 1.37365 \dots

Solution steps

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

Move

4

to the left side

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

Move

3 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.76803 \dots

Apply long division:

\frac{- 2 x ^{4} - 3 x + 3}{x - 0.76803 \dots} = - 2 x^{3} - 1.53606 \dots x^{2} - 1.17974 \dots x - 3.90608 \dots

- 2 x^{3} - 1.53606 \dots x^{2} - 1.17974 \dots x - 3.90608 \dots \approx 0

Find one solution for

- 2 x^{3} - 1.53606 \dots x^{2} - 1.17974 \dots x - 3.90608 \dots = 0

using Newton-Raphson:

x \approx - 1.37365 \dots

Apply long division:

\frac{- 2 x ^{3} - 1.53606 \dots x ^{2} - 1.17974 \dots x - 3.90608 \dots}{x + 1.37365 \dots} = - 2 x^{2} + 1.21124 \dots x - 2.84357 \dots

- 2 x^{2} + 1.21124 \dots x - 2.84357 \dots \approx 0

Find one solution for

- 2 x^{2} + 1.21124 \dots x - 2.84357 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.76803 \dots, x \approx - 1.37365 \dots

y^{4} - 7 y^{2} + 6 y^{1} = 0

9 x^{3} - 63 x^{2} - 16 x + 112 = 0

y^{4} - 6 y^{2} + 8 = 0

20000 = 5000 (1 + \frac{x}{2})^{20}

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

What are the solutions to the equation -2x^4+7=3x+4 ?
The solutions to the equation -2x^4+7=3x+4 are x\approx 0.76803…,x\approx-1.37365…
Find the zeros of -2x^4+7=3x+4
The zeros of -2x^4+7=3x+4 are x\approx 0.76803…,x\approx-1.37365…