What are the solutions to the equation x^3+6x^2-81=0 ?

The solutions to the equation x^3+6x^2-81=0 are x=3,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2

Find the zeros of x^3+6x^2-81=0

The zeros of x^3+6x^2-81=0 are x=3,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2

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x^{3} + 6 x^{2} - 81 = 0

x = 3, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

Solution steps

x^{3} + 6 x^{2} - 81 = 0

Factor

x^{3} + 6 x^{2} - 81 : (x - 3) (x^{2} + 9 x + 27)

(x - 3) (x^{2} + 9 x + 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 9 x + 27 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 9 x + 27 = 0 : x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

The solutions are

x = 3, x = - \frac{9}{2} + i \frac{3 3}{2}, x = - \frac{9}{2} - i \frac{3 3}{2}

x, x^{3} + y^{3} = 18

x, x^{3} = \frac{y}{2}

x (1 - \frac{x ^{3}}{2000}) = 0

2 x^{3} - 12 x^{2} + 16 x = 0

x, x^{3} + y^{3} = 36

What are the solutions to the equation x^3+6x^2-81=0 ?
The solutions to the equation x^3+6x^2-81=0 are x=3,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2
Find the zeros of x^3+6x^2-81=0
The zeros of x^3+6x^2-81=0 are x=3,x=-9/2+i(3sqrt(3))/2 ,x=-9/2-i(3sqrt(3))/2