What are the solutions to the equation x^2x+2=2(2-x)+6 ?

The solutions to the equation x^2x+2=2(2-x)+6 are x\approx 1.67024…

Find the zeros of x^2x+2=2(2-x)+6

The zeros of x^2x+2=2(2-x)+6 are x\approx 1.67024…

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x^{2} x + 2 = 2 (2 - x) + 6

x \approx 1.67024 \dots

Solution steps

x^{2} x + 2 = 2 (2 - x) + 6

Expand

x^{2} x + 2 : x^{3} + 2

Expand

2 (2 - x) + 6 : - 2 x + 10

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

Move

10

to the left side

x^{3} - 8 = - 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.67024 \dots

Apply long division:

\frac{x ^{3} + 2 x - 8}{x - 1.67024 \dots} = x^{2} + 1.67024 \dots x + 4.78971 \dots

x^{2} + 1.67024 \dots x + 4.78971 \dots \approx 0

Find one solution for

x^{2} + 1.67024 \dots x + 4.78971 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.67024 \dots

4 s^{3} + 7 s^{3} - 20 s - 35 = 0

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

z^{3} + 1 = e^{\frac{π}{2} i}

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) = 12

x^{4} - 5 x^{2} - 50 = 0

What are the solutions to the equation x^2x+2=2(2-x)+6 ?
The solutions to the equation x^2x+2=2(2-x)+6 are x\approx 1.67024…
Find the zeros of x^2x+2=2(2-x)+6
The zeros of x^2x+2=2(2-x)+6 are x\approx 1.67024…