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

The solutions to the equation 4x^1+4x^2+2x^3=4 are x\approx 0.57474…

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

The zeros of 4x^1+4x^2+2x^3=4 are x\approx 0.57474…

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

x \approx 0.57474 \dots

Solution steps

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

Refine

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

Move

4

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.57474 \dots

Apply long division:

\frac{2 x ^{3} + 4 x ^{2} + 4 x - 4}{x - 0.57474 \dots} = 2 x^{2} + 5.14948 \dots x + 6.95963 \dots

2 x^{2} + 5.14948 \dots x + 6.95963 \dots \approx 0

Find one solution for

2 x^{2} + 5.14948 \dots x + 6.95963 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.57474 \dots

5 x^{4} = 2560 x

2 r^{3} + 7 r^{2} - 4 r - 21 = 0

(1 + 0.0239193)^{1} = (1 + x)^{3}

8 x^{3} - 12 x^{2} + 6 x - 65 = 0

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

What are the solutions to the equation 4x^1+4x^2+2x^3=4 ?
The solutions to the equation 4x^1+4x^2+2x^3=4 are x\approx 0.57474…
Find the zeros of 4x^1+4x^2+2x^3=4
The zeros of 4x^1+4x^2+2x^3=4 are x\approx 0.57474…