What are the solutions to the equation (4x)/5-3=1+x^5+x-8 ?

The solutions to the equation (4x)/5-3=1+x^5+x-8 are x\approx 1.30186…

Find the zeros of (4x)/5-3=1+x^5+x-8

The zeros of (4x)/5-3=1+x^5+x-8 are x\approx 1.30186…

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\frac{4 x}{5} - 3 = 1 + x^{5} + x - 8

x \approx 1.30186 \dots

Solution steps

\frac{4 x}{5} - 3 = 1 + x^{5} + x - 8

Multiply both sides by

5

4 x - 15 = 5 + 5 x^{5} + 5 x - 40

4 x - 15 = 5 x^{5} + 5 x - 35

Switch sides

5 x^{5} + 5 x - 35 = 4 x - 15

Move

15

to the left side

5 x^{5} + 5 x - 20 = 4 x

Move

4 x

to the left side

5 x^{5} + x - 20 = 0

Find one solution for

5 x^{5} + x - 20 = 0

using Newton-Raphson:

x \approx 1.30186 \dots

Apply long division:

\frac{5 x ^{5} + x - 20}{x - 1.30186 \dots} = 5 x^{4} + 6.50932 \dots x^{3} + 8.47425 \dots x^{2} + 11.03232 \dots x + 15.36258 \dots

5 x^{4} + 6.50932 \dots x^{3} + 8.47425 \dots x^{2} + 11.03232 \dots x + 15.36258 \dots \approx 0

Find one solution for

5 x^{4} + 6.50932 \dots x^{3} + 8.47425 \dots x^{2} + 11.03232 \dots x + 15.36258 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.30186 \dots

x^{3} - 0.8 x^{2} - 0.04 x + 0.032 = 0

a^{6} = 64

x^{5} - 3 x^{4} + 1 = 0

8 x^{3} = - 64

x^{3} = x^{5} + x^{3} + x

What are the solutions to the equation (4x)/5-3=1+x^5+x-8 ?
The solutions to the equation (4x)/5-3=1+x^5+x-8 are x\approx 1.30186…
Find the zeros of (4x)/5-3=1+x^5+x-8
The zeros of (4x)/5-3=1+x^5+x-8 are x\approx 1.30186…