What are the solutions to the equation 2.08=x^3+x ?

The solutions to the equation 2.08=x^3+x are x\approx 1.01970…

Find the zeros of 2.08=x^3+x

The zeros of 2.08=x^3+x are x\approx 1.01970…

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2.08 = x^{3} + x

x \approx 1.01970 \dots

Solution steps

2.08 = x^{3} + x

Multiply both sides by

100

208 = x^{3} \cdot 100 + x \cdot 100

Switch sides

x^{3} \cdot 100 + x \cdot 100 = 208

Move

208

to the left side

x^{3} \cdot 100 + x \cdot 100 - 208 = 0

Write in the standard form

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

100 x^{3} + 100 x - 208 = 0

Find one solution for

100 x^{3} + 100 x - 208 = 0

using Newton-Raphson:

x \approx 1.01970 \dots

Apply long division:

\frac{100 x ^{3} + 100 x - 208}{x - 1.01970 \dots} = 100 x^{2} + 101.97068 \dots x + 203.98019 \dots

100 x^{2} + 101.97068 \dots x + 203.98019 \dots \approx 0

Find one solution for

100 x^{2} + 101.97068 \dots x + 203.98019 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.01970 \dots

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

x^{3} - x^{2} = - x

2 x^{3} + 5 x^{2} - 8 x - 20 = 0

6 x - 5 x^{2} - x^{3} = 0

(x + 1)^{2} - 3 x (x + 1)^{2} = 0

What are the solutions to the equation 2.08=x^3+x ?
The solutions to the equation 2.08=x^3+x are x\approx 1.01970…
Find the zeros of 2.08=x^3+x
The zeros of 2.08=x^3+x are x\approx 1.01970…