What are the solutions to the equation x+x^2+x^3=180 ?

The solutions to the equation x+x^2+x^3=180 are x\approx 5.27625…

Find the zeros of x+x^2+x^3=180

The zeros of x+x^2+x^3=180 are x\approx 5.27625…

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x + x^{2} + x^{3} = 180

x \approx 5.27625 \dots

Solution steps

x + x^{2} + x^{3} = 180

Move

180

to the left side

x + x^{2} + x^{3} - 180 = 0

Write in the standard form

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

x^{3} + x^{2} + x - 180 = 0

Find one solution for

x^{3} + x^{2} + x - 180 = 0

using Newton-Raphson:

x \approx 5.27625 \dots

Apply long division:

\frac{x ^{3} + x ^{2} + x - 180}{x - 5.27625 \dots} = x^{2} + 6.27625 \dots x + 34.11511 \dots

x^{2} + 6.27625 \dots x + 34.11511 \dots \approx 0

Find one solution for

x^{2} + 6.27625 \dots x + 34.11511 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 5.27625 \dots

2 x^{3} - 7 x^{2} - 12 x + 44 = 0

x^{4} - 6 x^{2} + 8 = 0

m^{4} - 4 m^{2} + 4 = 0

x, y = f (x^{4})

x^{3} - 9 x^{2} + 14 x + 24 = 0

What are the solutions to the equation x+x^2+x^3=180 ?
The solutions to the equation x+x^2+x^3=180 are x\approx 5.27625…
Find the zeros of x+x^2+x^3=180
The zeros of x+x^2+x^3=180 are x\approx 5.27625…