What are the solutions to the equation x^2-6=6-x^3 ?

The solutions to the equation x^2-6=6-x^3 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

Find the zeros of x^2-6=6-x^3

The zeros of x^2-6=6-x^3 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

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

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Solution steps

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

Switch sides

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

Move

6

to the left side

- x^{3} + 12 = x^{2}

Move

x^{2}

to the left side

- x^{3} + 12 - x^{2} = 0

Write in the standard form

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

- x^{3} - x^{2} + 12 = 0

Factor

- x^{3} - x^{2} + 12 : - (x - 2) (x^{2} + 3 x + 6)

- (x - 2) (x^{2} + 3 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 3 x + 6 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 3 x + 6 = 0 : x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

The solutions are

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

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

x^{10} = 3

(x - 1)^{3} = 17

(x - 1)^{3} = - 8

x^{3} + 2 x^{2} + 3 x + 1 = 0

What are the solutions to the equation x^2-6=6-x^3 ?
The solutions to the equation x^2-6=6-x^3 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2
Find the zeros of x^2-6=6-x^3
The zeros of x^2-6=6-x^3 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2