What are the solutions to the equation x^4x-8=2x-4 ?

The solutions to the equation x^4x-8=2x-4 are x\approx 1.47353…

Find the zeros of x^4x-8=2x-4

The zeros of x^4x-8=2x-4 are x\approx 1.47353…

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

x \approx 1.47353 \dots

Solution steps

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

Expand

x^{4} x - 8 : x^{5} - 8

x^{5} - 8 = 2 x - 4

Move

4

to the left side

x^{5} - 4 = 2 x

Move

2 x

to the left side

x^{5} - 4 - 2 x = 0

Write in the standard form

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

x^{5} - 2 x - 4 = 0

Find one solution for

x^{5} - 2 x - 4 = 0

using Newton-Raphson:

x \approx 1.47353 \dots

Apply long division:

\frac{x ^{5} - 2 x - 4}{x - 1.47353 \dots} = x^{4} + 1.47353 \dots x^{3} + 2.17130 \dots x^{2} + 3.19949 \dots x + 2.71456 \dots

x^{4} + 1.47353 \dots x^{3} + 2.17130 \dots x^{2} + 3.19949 \dots x + 2.71456 \dots \approx 0

Find one solution for

x^{4} + 1.47353 \dots x^{3} + 2.17130 \dots x^{2} + 3.19949 \dots x + 2.71456 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.47353 \dots

x (x^{2} + x - 6) = 0

- 2 = 2 x^{5} + x^{3} + 1

(2 - x^{2})^{2} - 1 = 0

m^{4} - 13 m^{2} + 36 = 0

z^{4} + 3 z^{2} + 2 = 0

What are the solutions to the equation x^4x-8=2x-4 ?
The solutions to the equation x^4x-8=2x-4 are x\approx 1.47353…
Find the zeros of x^4x-8=2x-4
The zeros of x^4x-8=2x-4 are x\approx 1.47353…