What are the solutions to the equation 5=4x^3+12x^2+12x+4 ?

The solutions to the equation 5=4x^3+12x^2+12x+4 are x\approx 0.07721…

Find the zeros of 5=4x^3+12x^2+12x+4

The zeros of 5=4x^3+12x^2+12x+4 are x\approx 0.07721…

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5 = 4 x^{3} + 12 x^{2} + 12 x + 4

x \approx 0.07721 \dots

Solution steps

5 = 4 x^{3} + 12 x^{2} + 12 x + 4

Switch sides

4 x^{3} + 12 x^{2} + 12 x + 4 = 5

Move

5

to the left side

4 x^{3} + 12 x^{2} + 12 x - 1 = 0

Find one solution for

4 x^{3} + 12 x^{2} + 12 x - 1 = 0

using Newton-Raphson:

x \approx 0.07721 \dots

Apply long division:

\frac{4 x ^{3} + 12 x ^{2} + 12 x - 1}{x - 0.07721 \dots} = 4 x^{2} + 12.30886 \dots x + 12.95045 \dots

4 x^{2} + 12.30886 \dots x + 12.95045 \dots \approx 0

Find one solution for

4 x^{2} + 12.30886 \dots x + 12.95045 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.07721 \dots

(m - 1)^{2} (m^{2} + 1)^{2} = 0

x^{3} + 6 x + 9 x = 0

2 x^{4} = 128 x

x, 2 x y - x^{3} = 0

- 2 x^{3} + 3 = 0

What are the solutions to the equation 5=4x^3+12x^2+12x+4 ?
The solutions to the equation 5=4x^3+12x^2+12x+4 are x\approx 0.07721…
Find the zeros of 5=4x^3+12x^2+12x+4
The zeros of 5=4x^3+12x^2+12x+4 are x\approx 0.07721…