What are the solutions to the equation 4x^2+8x^4=(x^2+2x+1) ?

The solutions to the equation 4x^2+8x^4=(x^2+2x+1) are x\approx-0.31368…,x\approx 0.60955…

Find the zeros of 4x^2+8x^4=(x^2+2x+1)

The zeros of 4x^2+8x^4=(x^2+2x+1) are x\approx-0.31368…,x\approx 0.60955…

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4 x^{2} + 8 x^{4} = (x^{2} + 2 x + 1)

x \approx - 0.31368 \dots, x \approx 0.60955 \dots

Solution steps

4 x^{2} + 8 x^{4} = (x^{2} + 2 x + 1)

Refine

4 x^{2} + 8 x^{4} = x^{2} + 2 x + 1

Move

1

to the left side

4 x^{2} + 8 x^{4} - 1 = x^{2} + 2 x

Move

2 x

to the left side

4 x^{2} + 8 x^{4} - 1 - 2 x = x^{2}

Move

x^{2}

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.31368 \dots

Apply long division:

\frac{8 x ^{4} + 3 x ^{2} - 2 x - 1}{x + 0.31368 \dots} = 8 x^{3} - 2.50944 \dots x^{2} + 3.78716 \dots x - 3.18795 \dots

8 x^{3} - 2.50944 \dots x^{2} + 3.78716 \dots x - 3.18795 \dots \approx 0

Find one solution for

8 x^{3} - 2.50944 \dots x^{2} + 3.78716 \dots x - 3.18795 \dots = 0

using Newton-Raphson:

x \approx 0.60955 \dots

Apply long division:

\frac{8 x ^{3} - 2.50944 \dots x ^{2} + 3.78716 \dots x - 3.18795 \dots}{x - 0.60955 \dots} = 8 x^{2} + 2.36699 \dots x + 5.22997 \dots

8 x^{2} + 2.36699 \dots x + 5.22997 \dots \approx 0

Find one solution for

8 x^{2} + 2.36699 \dots x + 5.22997 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.31368 \dots, x \approx 0.60955 \dots

4 x^{3} - 27 x^{2} - 11 x - 1 = 0

(1 - m)^{3} = \frac{1}{3}

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

4 x^{3} - 54 x^{2} + 180 x - 125 = 0

2 k^{3} - 8 k^{2} + 2 k + 1 = 0

What are the solutions to the equation 4x^2+8x^4=(x^2+2x+1) ?
The solutions to the equation 4x^2+8x^4=(x^2+2x+1) are x\approx-0.31368…,x\approx 0.60955…
Find the zeros of 4x^2+8x^4=(x^2+2x+1)
The zeros of 4x^2+8x^4=(x^2+2x+1) are x\approx-0.31368…,x\approx 0.60955…