What are the solutions to the equation (x+2)+(x^2-4x+4)-x^2(x-2)=-53 ?

The solutions to the equation (x+2)+(x^2-4x+4)-x^2(x-2)=-53 are x\approx 4.87087…

Find the zeros of (x+2)+(x^2-4x+4)-x^2(x-2)=-53

The zeros of (x+2)+(x^2-4x+4)-x^2(x-2)=-53 are x\approx 4.87087…

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(x + 2) + (x^{2} - 4 x + 4) - x^{2} (x - 2) = - 53

x \approx 4.87087 \dots

Solution steps

(x + 2) + (x^{2} - 4 x + 4) - x^{2} (x - 2) = - 53

Expand

(x + 2) + (x^{2} - 4 x + 4) - x^{2} (x - 2) : - x^{3} + 3 x^{2} - 3 x + 6

- x^{3} + 3 x^{2} - 3 x + 6 = - 53

Move

53

to the left side

- x^{3} + 3 x^{2} - 3 x + 59 = 0

Find one solution for

- x^{3} + 3 x^{2} - 3 x + 59 = 0

using Newton-Raphson:

x \approx 4.87087 \dots

Apply long division:

\frac{- x ^{3} + 3 x ^{2} - 3 x + 59}{x - 4.87087 \dots} = - x^{2} - 1.87087 \dots x - 12.11280 \dots

- x^{2} - 1.87087 \dots x - 12.11280 \dots \approx 0

Find one solution for

- x^{2} - 1.87087 \dots x - 12.11280 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 4.87087 \dots

64 x^{3} + 1 = 0

x^{6} + 6 x^{3} + 9 = 0

d^{3} - 6 d^{2} + 11 d - 6 = 0

x^{100} = 1

3 x^{4} = 48 x^{2}

What are the solutions to the equation (x+2)+(x^2-4x+4)-x^2(x-2)=-53 ?
The solutions to the equation (x+2)+(x^2-4x+4)-x^2(x-2)=-53 are x\approx 4.87087…
Find the zeros of (x+2)+(x^2-4x+4)-x^2(x-2)=-53
The zeros of (x+2)+(x^2-4x+4)-x^2(x-2)=-53 are x\approx 4.87087…