What are the solutions to the equation x+x^2+400x^3=11500 ?

The solutions to the equation x+x^2+400x^3=11500 are x\approx 3.06235…

Find the zeros of x+x^2+400x^3=11500

The zeros of x+x^2+400x^3=11500 are x\approx 3.06235…

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x + x^{2} + 400 x^{3} = 11500

x \approx 3.06235 \dots

Solution steps

x + x^{2} + 400 x^{3} = 11500

Move

11500

to the left side

x + x^{2} + 400 x^{3} - 11500 = 0

Write in the standard form

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

400 x^{3} + x^{2} + x - 11500 = 0

Find one solution for

400 x^{3} + x^{2} + x - 11500 = 0

using Newton-Raphson:

x \approx 3.06235 \dots

Apply long division:

\frac{400 x ^{3} + x ^{2} + x - 11500}{x - 3.06235 \dots} = 400 x^{2} + 1225.94311 \dots x + 3755.27643 \dots

400 x^{2} + 1225.94311 \dots x + 3755.27643 \dots \approx 0

Find one solution for

400 x^{2} + 1225.94311 \dots x + 3755.27643 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 3.06235 \dots

6 x^{4} - x^{3} - 22 x^{2} + 11 x + 6 = 0

4 x^{4} - 349 x^{2} + 2025 = 0

y, x^{3} + y^{3} = x

- 2 x^{3} - 9 x^{2} - 12 x - 4 = 0

x^{3} + 2 x = 3

What are the solutions to the equation x+x^2+400x^3=11500 ?
The solutions to the equation x+x^2+400x^3=11500 are x\approx 3.06235…
Find the zeros of x+x^2+400x^3=11500
The zeros of x+x^2+400x^3=11500 are x\approx 3.06235…