What are the solutions to the equation x^3=6x+9 ?

The solutions to the equation x^3=6x+9 are x=3,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2

Find the zeros of x^3=6x+9

The zeros of x^3=6x+9 are x=3,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2

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x^{3} = 6 x + 9

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

Solution steps

x^{3} = 6 x + 9

Move

9

to the left side

x^{3} - 9 = 6 x

Move

6 x

to the left side

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

Write in the standard form

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

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

Factor

x^{3} - 6 x - 9 : (x - 3) (x^{2} + 3 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

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

a, a^{2} (ba - b + 1 - a^{2}) = 0

m^{3} + 2 m^{2} + 4 m + 8 = 0

5 x^{4} - 1 = 0

- 4 x^{3} - 16 x = 0

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

What are the solutions to the equation x^3=6x+9 ?
The solutions to the equation x^3=6x+9 are x=3,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2
Find the zeros of x^3=6x+9
The zeros of x^3=6x+9 are x=3,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2