What are the solutions to the equation x-13+x^4=2 ?

The solutions to the equation x-13+x^4=2 are x\approx 1.90238…,x\approx-2.03148…

Find the zeros of x-13+x^4=2

The zeros of x-13+x^4=2 are x\approx 1.90238…,x\approx-2.03148…

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x - 13 + x^{4} = 2

x \approx 1.90238 \dots, x \approx - 2.03148 \dots

Solution steps

x - 13 + x^{4} = 2

Move

2

to the left side

x^{4} + x - 15 = 0

Find one solution for

x^{4} + x - 15 = 0

using Newton-Raphson:

x \approx 1.90238 \dots

Apply long division:

\frac{x ^{4} + x - 15}{x - 1.90238 \dots} = x^{3} + 1.90238 \dots x^{2} + 3.61906 \dots x + 7.88484 \dots

x^{3} + 1.90238 \dots x^{2} + 3.61906 \dots x + 7.88484 \dots \approx 0

Find one solution for

x^{3} + 1.90238 \dots x^{2} + 3.61906 \dots x + 7.88484 \dots = 0

using Newton-Raphson:

x \approx - 2.03148 \dots

Apply long division:

\frac{x ^{3} + 1.90238 \dots x ^{2} + 3.61906 \dots x + 7.88484 \dots}{x + 2.03148 \dots} = x^{2} - 0.12909 \dots x + 3.88132 \dots

x^{2} - 0.12909 \dots x + 3.88132 \dots \approx 0

Find one solution for

x^{2} - 0.12909 \dots x + 3.88132 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.90238 \dots, x \approx - 2.03148 \dots

x^{6} + 5 = 13 - x

- 4 x^{3} + 36 x = 0

x^{3} + x^{2} - 120 = 0

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

4 x^{3} + 12 x^{2} + 18 x + 10 = 0

What are the solutions to the equation x-13+x^4=2 ?
The solutions to the equation x-13+x^4=2 are x\approx 1.90238…,x\approx-2.03148…
Find the zeros of x-13+x^4=2
The zeros of x-13+x^4=2 are x\approx 1.90238…,x\approx-2.03148…