What are the solutions to the equation x^4=16-x^3 ?

The solutions to the equation x^4=16-x^3 are x\approx 1.78995…,x\approx-2.30555…

Find the zeros of x^4=16-x^3

The zeros of x^4=16-x^3 are x\approx 1.78995…,x\approx-2.30555…

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x^{4} = 16 - x^{3}

x \approx 1.78995 \dots, x \approx - 2.30555 \dots

Solution steps

x^{4} = 16 - x^{3}

Move

x^{3}

to the left side

x^{4} + x^{3} = 16

Move

16

to the left side

x^{4} + x^{3} - 16 = 0

Find one solution for

x^{4} + x^{3} - 16 = 0

using Newton-Raphson:

x \approx 1.78995 \dots

Apply long division:

\frac{x ^{4} + x ^{3} - 16}{x - 1.78995 \dots} = x^{3} + 2.78995 \dots x^{2} + 4.99387 \dots x + 8.93879 \dots

x^{3} + 2.78995 \dots x^{2} + 4.99387 \dots x + 8.93879 \dots \approx 0

Find one solution for

x^{3} + 2.78995 \dots x^{2} + 4.99387 \dots x + 8.93879 \dots = 0

using Newton-Raphson:

x \approx - 2.30555 \dots

Apply long division:

\frac{x ^{3} + 2.78995 \dots x ^{2} + 4.99387 \dots x + 8.93879 \dots}{x + 2.30555 \dots} = x^{2} + 0.48439 \dots x + 3.87707 \dots

x^{2} + 0.48439 \dots x + 3.87707 \dots \approx 0

Find one solution for

x^{2} + 0.48439 \dots x + 3.87707 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.78995 \dots, x \approx - 2.30555 \dots

x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12 = 0

x^{3} - 7 x^{2} + 10 x = 0

x^{3} + 2 x^{2} - 9 x = 18

4 x^{3} - 19 x^{2} - 5 x = 0

9.6 t - 0.6 t^{5} = 0

What are the solutions to the equation x^4=16-x^3 ?
The solutions to the equation x^4=16-x^3 are x\approx 1.78995…,x\approx-2.30555…
Find the zeros of x^4=16-x^3
The zeros of x^4=16-x^3 are x\approx 1.78995…,x\approx-2.30555…