What are the solutions to the equation x^4x+8=8x+16 ?

The solutions to the equation x^4x+8=8x+16 are x\approx 1.87174…

Find the zeros of x^4x+8=8x+16

The zeros of x^4x+8=8x+16 are x\approx 1.87174…

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x^{4} x + 8 = 8 x + 16

x \approx 1.87174 \dots

Solution steps

x^{4} x + 8 = 8 x + 16

Expand

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

x^{5} + 8 = 8 x + 16

Move

16

to the left side

x^{5} - 8 = 8 x

Move

8 x

to the left side

x^{5} - 8 - 8 x = 0

Write in the standard form

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

x^{5} - 8 x - 8 = 0

Find one solution for

x^{5} - 8 x - 8 = 0

using Newton-Raphson:

x \approx 1.87174 \dots

Apply long division:

\frac{x ^{5} - 8 x - 8}{x - 1.87174 \dots} = x^{4} + 1.87174 \dots x^{3} + 3.50343 \dots x^{2} + 6.55755 \dots x + 4.27408 \dots

x^{4} + 1.87174 \dots x^{3} + 3.50343 \dots x^{2} + 6.55755 \dots x + 4.27408 \dots \approx 0

Find one solution for

x^{4} + 1.87174 \dots x^{3} + 3.50343 \dots x^{2} + 6.55755 \dots x + 4.27408 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.87174 \dots

2 x^{5} - 12 x^{3} = - 16 x

- λ^{3} - 13 λ^{2} - 56 λ - 80 = 0

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

x^{3} - 10 x^{2} + 28 x + 24 = 0

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

What are the solutions to the equation x^4x+8=8x+16 ?
The solutions to the equation x^4x+8=8x+16 are x\approx 1.87174…
Find the zeros of x^4x+8=8x+16
The zeros of x^4x+8=8x+16 are x\approx 1.87174…