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

The solutions to the equation x^2+2=x^3-x are x=2,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

Find the zeros of x^2+2=x^3-x

The zeros of x^2+2=x^3-x are x=2,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

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

x = 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Switch sides

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

Move

2

to the left side

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

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Factor

x^{3} - x^{2} - x - 2 : (x - 2) (x^{2} + x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + x + 1 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

The solutions are

x = 2, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

z^{8} - 8 = 0

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

7 = 10 - 3 m^{3}

s^{3} + 10.5 s^{2} + 90 s + 127.5 = 0

3 x^{5} - 2 x^{3} + 15 = 0

What are the solutions to the equation x^2+2=x^3-x ?
The solutions to the equation x^2+2=x^3-x are x=2,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2
Find the zeros of x^2+2=x^3-x
The zeros of x^2+2=x^3-x are x=2,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2