What are the solutions to the equation x^3-27x-27=0 ?

The solutions to the equation x^3-27x-27=0 are x\approx-1.04188…,x\approx-4.59626…,x\approx 5.63815…

Find the zeros of x^3-27x-27=0

The zeros of x^3-27x-27=0 are x\approx-1.04188…,x\approx-4.59626…,x\approx 5.63815…

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x^{3} - 27 x - 27 = 0

x \approx - 1.04188 \dots, x \approx - 4.59626 \dots, x \approx 5.63815 \dots

Solution steps

x^{3} - 27 x - 27 = 0

Find one solution for

x^{3} - 27 x - 27 = 0

using Newton-Raphson:

x \approx - 1.04188 \dots

Apply long division:

\frac{x ^{3} - 27 x - 27}{x + 1.04188 \dots} = x^{2} - 1.04188 \dots x - 25.91446 \dots

x^{2} - 1.04188 \dots x - 25.91446 \dots \approx 0

Find one solution for

x^{2} - 1.04188 \dots x - 25.91446 \dots = 0

using Newton-Raphson:

x \approx - 4.59626 \dots

Apply long division:

\frac{x ^{2} - 1.04188 \dots x - 25.91446 \dots}{x + 4.59626 \dots} = x - 5.63815 \dots

x - 5.63815 \dots \approx 0

x \approx 5.63815 \dots

The solutions are

x \approx - 1.04188 \dots, x \approx - 4.59626 \dots, x \approx 5.63815 \dots

x^{3} + 5 x^{2} + 6 x = - 30

4 (x + 4)^{4} - 53 (x + 4)^{2} = - 49

0 = x^{3} - 2 x^{2} - 11 x + 12

a \cdot a \cdot a = 3 a

2 x^{3} + 3 x^{2} - 17 x + 12 = 0

What are the solutions to the equation x^3-27x-27=0 ?
The solutions to the equation x^3-27x-27=0 are x\approx-1.04188…,x\approx-4.59626…,x\approx 5.63815…
Find the zeros of x^3-27x-27=0
The zeros of x^3-27x-27=0 are x\approx-1.04188…,x\approx-4.59626…,x\approx 5.63815…