What are the solutions to the equation x+x^2+600x^3=14500 ?

The solutions to the equation x+x^2+600x^3=14500 are x\approx 2.89041…

Find the zeros of x+x^2+600x^3=14500

The zeros of x+x^2+600x^3=14500 are x\approx 2.89041…

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x + x^{2} + 600 x^{3} = 14500

x \approx 2.89041 \dots

Solution steps

x + x^{2} + 600 x^{3} = 14500

Move

14500

to the left side

x + x^{2} + 600 x^{3} - 14500 = 0

Write in the standard form

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

600 x^{3} + x^{2} + x - 14500 = 0

Find one solution for

600 x^{3} + x^{2} + x - 14500 = 0

using Newton-Raphson:

x \approx 2.89041 \dots

Apply long division:

\frac{600 x ^{3} + x ^{2} + x - 14500}{x - 2.89041 \dots} = 600 x^{2} + 1735.24795 \dots x + 5016.58368 \dots

600 x^{2} + 1735.24795 \dots x + 5016.58368 \dots \approx 0

Find one solution for

600 x^{2} + 1735.24795 \dots x + 5016.58368 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.89041 \dots

(\frac{6 a}{7})^{3} = 1728

16 x (x + 1) (x + 2) (x + 3) = 105

x^{3} = \frac{125}{27}

10 = 500 b^{3}

(x^{2} - 9)^{2} - x^{2} + 10 = 1

What are the solutions to the equation x+x^2+600x^3=14500 ?
The solutions to the equation x+x^2+600x^3=14500 are x\approx 2.89041…
Find the zeros of x+x^2+600x^3=14500
The zeros of x+x^2+600x^3=14500 are x\approx 2.89041…