What are the solutions to the equation 2x^3+4x^2=1 ?

The solutions to the equation 2x^3+4x^2=1 are x\approx 0.45160…,x\approx-0.59696…,x\approx-1.85463…

Find the zeros of 2x^3+4x^2=1

The zeros of 2x^3+4x^2=1 are x\approx 0.45160…,x\approx-0.59696…,x\approx-1.85463…

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2 x^{3} + 4 x^{2} = 1

x \approx 0.45160 \dots, x \approx - 0.59696 \dots, x \approx - 1.85463 \dots

Solution steps

2 x^{3} + 4 x^{2} = 1

Move

1

to the left side

2 x^{3} + 4 x^{2} - 1 = 0

Find one solution for

2 x^{3} + 4 x^{2} - 1 = 0

using Newton-Raphson:

x \approx 0.45160 \dots

Apply long division:

\frac{2 x ^{3} + 4 x ^{2} - 1}{x - 0.45160 \dots} = 2 x^{2} + 4.90321 \dots x + 2.21431 \dots

2 x^{2} + 4.90321 \dots x + 2.21431 \dots \approx 0

Find one solution for

2 x^{2} + 4.90321 \dots x + 2.21431 \dots = 0

using Newton-Raphson:

x \approx - 0.59696 \dots

Apply long division:

\frac{2 x ^{2} + 4.90321 \dots x + 2.21431 \dots}{x + 0.59696 \dots} = 2 x + 3.70927 \dots

2 x + 3.70927 \dots \approx 0

x \approx - 1.85463 \dots

The solutions are

x \approx 0.45160 \dots, x \approx - 0.59696 \dots, x \approx - 1.85463 \dots

(6 - x)^{4} + (8 - x)^{4} = 16

x^{5} - 1 = 0

x^{4} - 8 x^{2} = - 16

x^{3} - 6 x^{3} + 3 x + 10 = 0

x^{3} + 2 x^{2} - 9 x - 18 = 0

What are the solutions to the equation 2x^3+4x^2=1 ?
The solutions to the equation 2x^3+4x^2=1 are x\approx 0.45160…,x\approx-0.59696…,x\approx-1.85463…
Find the zeros of 2x^3+4x^2=1
The zeros of 2x^3+4x^2=1 are x\approx 0.45160…,x\approx-0.59696…,x\approx-1.85463…