What are the solutions to the equation x^3+2x^2+10x=20 ?

The solutions to the equation x^3+2x^2+10x=20 are x\approx 1.36880…

Find the zeros of x^3+2x^2+10x=20

The zeros of x^3+2x^2+10x=20 are x\approx 1.36880…

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x^{3} + 2 x^{2} + 10 x = 20

x \approx 1.36880 \dots

Solution steps

x^{3} + 2 x^{2} + 10 x = 20

Move

20

to the left side

x^{3} + 2 x^{2} + 10 x - 20 = 0

Find one solution for

x^{3} + 2 x^{2} + 10 x - 20 = 0

using Newton-Raphson:

x \approx 1.36880 \dots

Apply long division:

\frac{x ^{3} + 2 x ^{2} + 10 x - 20}{x - 1.36880 \dots} = x^{2} + 3.36880 \dots x + 14.61125 \dots

x^{2} + 3.36880 \dots x + 14.61125 \dots \approx 0

Find one solution for

x^{2} + 3.36880 \dots x + 14.61125 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.36880 \dots

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

d^{4} - 1 = 0

x^{2} + 4 x^{3} + 5 x^{2} + 2 x^{2} = 0

\frac{3 ( n + 1 ) n ( n - 1 )}{6} = \frac{n ( n - 1 )}{2}

(x + 6)^{3} = - 27

What are the solutions to the equation x^3+2x^2+10x=20 ?
The solutions to the equation x^3+2x^2+10x=20 are x\approx 1.36880…
Find the zeros of x^3+2x^2+10x=20
The zeros of x^3+2x^2+10x=20 are x\approx 1.36880…