What are the solutions to the equation x^5+2x-7=50 ?

The solutions to the equation x^5+2x-7=50 are x\approx 2.20885…

Find the zeros of x^5+2x-7=50

The zeros of x^5+2x-7=50 are x\approx 2.20885…

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x^{5} + 2 x - 7 = 50

x \approx 2.20885 \dots

Solution steps

x^{5} + 2 x - 7 = 50

Move

50

to the left side

x^{5} + 2 x - 57 = 0

Find one solution for

x^{5} + 2 x - 57 = 0

using Newton-Raphson:

x \approx 2.20885 \dots

Apply long division:

\frac{x ^{5} + 2 x - 57}{x - 2.20885 \dots} = x^{4} + 2.20885 \dots x^{3} + 4.87905 \dots x^{2} + 10.77714 \dots x + 25.80518 \dots

x^{4} + 2.20885 \dots x^{3} + 4.87905 \dots x^{2} + 10.77714 \dots x + 25.80518 \dots \approx 0

Find one solution for

x^{4} + 2.20885 \dots x^{3} + 4.87905 \dots x^{2} + 10.77714 \dots x + 25.80518 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.20885 \dots

u^{4} - u^{2} + 1 = 0

3 x^{4} + 26 = 19 x^{2}

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

x (x^{2} + 5 x + 8) = 0

x^{3} - 9 x^{2} + 14 x = 0

What are the solutions to the equation x^5+2x-7=50 ?
The solutions to the equation x^5+2x-7=50 are x\approx 2.20885…
Find the zeros of x^5+2x-7=50
The zeros of x^5+2x-7=50 are x\approx 2.20885…