What are the solutions to the equation x^3(22-(x/2))=18 ?

The solutions to the equation x^3(22-(x/2))=18 are x\approx 0.94206…,x\approx 43.99957…

Find the zeros of x^3(22-(x/2))=18

The zeros of x^3(22-(x/2))=18 are x\approx 0.94206…,x\approx 43.99957…

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x^{3} (22 - (\frac{x}{2})) = 18

x \approx 0.94206 \dots, x \approx 43.99957 \dots

Solution steps

x^{3} (22 - (\frac{x}{2})) = 18

Expand

x^{3} (22 - (\frac{x}{2})) : 22 x^{3} - \frac{x ^{4}}{2}

22 x^{3} - \frac{x ^{4}}{2} = 18

Move

18

to the left side

22 x^{3} - \frac{x ^{4}}{2} - 18 = 0

Write in the standard form

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

- \frac{x ^{4}}{2} + 22 x^{3} - 18 = 0

Find one solution for

- 0.5 x^{4} + 22 x^{3} - 18 = 0

using Newton-Raphson:

x \approx 0.94206 \dots

Apply long division:

\frac{- \frac{x ^{4}}{2} + 22 x ^{3} - 18}{x - 0.94206 \dots} = - 0.5 x^{3} + 21.52896 \dots x^{2} + 20.28178 \dots x + 19.10686 \dots

- 0.5 x^{3} + 21.52896 \dots x^{2} + 20.28178 \dots x + 19.10686 \dots \approx 0

Find one solution for

- 0.5 x^{3} + 21.52896 \dots x^{2} + 20.28178 \dots x + 19.10686 \dots = 0

using Newton-Raphson:

x \approx 43.99957 \dots

Apply long division:

\frac{- 0.5 x ^{3} + 21.52896 \dots x ^{2} + 20.28178 \dots x + 19.10686 \dots}{x - 43.99957 \dots} = - 0.5 x^{2} - 0.47082 \dots x - 0.43425 \dots

- 0.5 x^{2} - 0.47082 \dots x - 0.43425 \dots \approx 0

Find one solution for

- 0.5 x^{2} - 0.47082 \dots x - 0.43425 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.94206 \dots, x \approx 43.99957 \dots

4 x (x - 1)^{2} = 1

(x + 1) (x + 2)^{2} (x^{2} - 6 x + 10) = 0

4 x^{3} - 3 x = 0

s^{3} = 1000

(2 A + 1) A^{66} = 0

What are the solutions to the equation x^3(22-(x/2))=18 ?
The solutions to the equation x^3(22-(x/2))=18 are x\approx 0.94206…,x\approx 43.99957…
Find the zeros of x^3(22-(x/2))=18
The zeros of x^3(22-(x/2))=18 are x\approx 0.94206…,x\approx 43.99957…