What are the solutions to the equation (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 ?

The solutions to the equation (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 are x\approx 4.09477…

Find the zeros of (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64

The zeros of (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 are x\approx 4.09477…

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(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) = 64

x \approx 4.09477 \dots

Solution steps

(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) = 64

Expand

(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) : x^{3} - 0.3 x^{2} + 0.1 x - 0.03703 \dots

x^{3} - 0.3 x^{2} + 0.1 x - 0.03703 \dots = 64

Move

64

to the left side

x^{3} - 0.3 x^{2} + 0.1 x - 64.03703 \dots = 0

Find one solution for

x^{3} - 0.3 x^{2} + 0.1 x - 64.03703 \dots = 0

using Newton-Raphson:

x \approx 4.09477 \dots

Apply long division:

\frac{x ^{3} - 0.3 x ^{2} + 0.1 x - 64.03703 \dots}{x - 4.09477 \dots} = x^{2} + 3.79477 \dots x + 15.63872 \dots

x^{2} + 3.79477 \dots x + 15.63872 \dots \approx 0

Find one solution for

x^{2} + 3.79477 \dots x + 15.63872 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 4.09477 \dots

(x - 7)^{4} = (x - 7)^{5}

x^{3} = - 125

(x + 5) (x^{2} - 4) = 0

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6 = 0

n^{3} - n - 990 = 0

What are the solutions to the equation (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 ?
The solutions to the equation (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 are x\approx 4.09477…
Find the zeros of (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64
The zeros of (x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64 are x\approx 4.09477…