What are the solutions to the equation x+(2x^2-3)^3=0 ?

The solutions to the equation x+(2x^2-3)^3=0 are x\approx 1.00000…,x\approx-1.43673…

Find the zeros of x+(2x^2-3)^3=0

The zeros of x+(2x^2-3)^3=0 are x\approx 1.00000…,x\approx-1.43673…

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

x \approx 1.00000 \dots, x \approx - 1.43673 \dots

Solution steps

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

Expand

x + (2 x^{2} - 3)^{3} : x + 8 x^{6} - 36 x^{4} + 54 x^{2} - 27

x + 8 x^{6} - 36 x^{4} + 54 x^{2} - 27 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

8 x^{6} - 36 x^{4} + 54 x^{2} + x - 27 = 0

Find one solution for

8 x^{6} - 36 x^{4} + 54 x^{2} + x - 27 = 0

using Newton-Raphson:

x \approx 1.00000 \dots

Apply long division:

\frac{8 x ^{6} - 36 x ^{4} + 54 x ^{2} + x - 27}{x - 1} = 8 x^{5} + 8 x^{4} - 28 x^{3} - 28 x^{2} + 26 x + 27

8 x^{5} + 8 x^{4} - 28 x^{3} - 28 x^{2} + 26 x + 27 \approx 0

Find one solution for

8 x^{5} + 8 x^{4} - 28 x^{3} - 28 x^{2} + 26 x + 27 = 0

using Newton-Raphson:

x \approx - 1.43673 \dots

Apply long division:

\frac{8 x ^{5} + 8 x ^{4} - 28 x ^{3} - 28 x ^{2} + 26 x + 27}{x + 1.43673 \dots} = 8 x^{4} - 3.49384 \dots x^{3} - 22.98029 \dots x^{2} + 5.01648 \dots x + 18.79267 \dots

8 x^{4} - 3.49384 \dots x^{3} - 22.98029 \dots x^{2} + 5.01648 \dots x + 18.79267 \dots \approx 0

Find one solution for

8 x^{4} - 3.49384 \dots x^{3} - 22.98029 \dots x^{2} + 5.01648 \dots x + 18.79267 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1, x \approx - 1.43673 \dots

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

x^{4} - 5 x^{2} - 36

x^{3} - 81 = 0

x (x - 1) (x + 2) - 2 = 0

x^{3} - 31 x - 30 = 0

What are the solutions to the equation x+(2x^2-3)^3=0 ?
The solutions to the equation x+(2x^2-3)^3=0 are x\approx 1.00000…,x\approx-1.43673…
Find the zeros of x+(2x^2-3)^3=0
The zeros of x+(2x^2-3)^3=0 are x\approx 1.00000…,x\approx-1.43673…