What are the solutions to the equation x^3=1+14x ?

The solutions to the equation x^3=1+14x are x\approx-0.07145…,x\approx 3.77687…,x\approx-3.70541…

Find the zeros of x^3=1+14x

The zeros of x^3=1+14x are x\approx-0.07145…,x\approx 3.77687…,x\approx-3.70541…

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x^{3} = 1 + 14 x

x \approx - 0.07145 \dots, x \approx 3.77687 \dots, x \approx - 3.70541 \dots

Solution steps

x^{3} = 1 + 14 x

Move

14 x

to the left side

x^{3} - 14 x = 1

Move

1

to the left side

x^{3} - 14 x - 1 = 0

Find one solution for

x^{3} - 14 x - 1 = 0

using Newton-Raphson:

x \approx - 0.07145 \dots

Apply long division:

\frac{x ^{3} - 14 x - 1}{x + 0.07145 \dots} = x^{2} - 0.07145 \dots x - 13.99489 \dots

x^{2} - 0.07145 \dots x - 13.99489 \dots \approx 0

Find one solution for

x^{2} - 0.07145 \dots x - 13.99489 \dots = 0

using Newton-Raphson:

x \approx 3.77687 \dots

Apply long division:

\frac{x ^{2} - 0.07145 \dots x - 13.99489 \dots}{x - 3.77687 \dots} = x + 3.70541 \dots

x + 3.70541 \dots \approx 0

x \approx - 3.70541 \dots

The solutions are

x \approx - 0.07145 \dots, x \approx 3.77687 \dots, x \approx - 3.70541 \dots

x^{4} + 9 x^{2} + 14 = 0

(x^{3} + 8) = 0

2 x^{4} - 7 x^{2} + 5 = 0

5 x^{4} - 8 x^{3} = 0

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

What are the solutions to the equation x^3=1+14x ?
The solutions to the equation x^3=1+14x are x\approx-0.07145…,x\approx 3.77687…,x\approx-3.70541…
Find the zeros of x^3=1+14x
The zeros of x^3=1+14x are x\approx-0.07145…,x\approx 3.77687…,x\approx-3.70541…