What are the solutions to the equation 0=x^3+21x-90 ?

The solutions to the equation 0=x^3+21x-90 are x=3,x=-3/2+i(sqrt(111))/2 ,x=-3/2-i(sqrt(111))/2

Find the zeros of 0=x^3+21x-90

The zeros of 0=x^3+21x-90 are x=3,x=-3/2+i(sqrt(111))/2 ,x=-3/2-i(sqrt(111))/2

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0 = x^{3} + 21 x - 90

x = 3, x = - \frac{3}{2} + i \frac{111}{2}, x = - \frac{3}{2} - i \frac{111}{2}

Solution steps

0 = x^{3} + 21 x - 90

Switch sides

x^{3} + 21 x - 90 = 0

Factor

x^{3} + 21 x - 90 : (x - 3) (x^{2} + 3 x + 30)

(x - 3) (x^{2} + 3 x + 30) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 3 x + 30 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 3 x + 30 = 0 : x = - \frac{3}{2} + i \frac{111}{2}, x = - \frac{3}{2} - i \frac{111}{2}

The solutions are

x = 3, x = - \frac{3}{2} + i \frac{111}{2}, x = - \frac{3}{2} - i \frac{111}{2}

(9 x^{3} + 6 x^{2} - 48 x + 10) = - 10

624 = 300 x + 3 x^{3}

(x - 1)^{3} = 8

x^{3} - 15 x^{2} + 63 x - 49 = 0

x^{3} - 14 x - 8 = 0

What are the solutions to the equation 0=x^3+21x-90 ?
The solutions to the equation 0=x^3+21x-90 are x=3,x=-3/2+i(sqrt(111))/2 ,x=-3/2-i(sqrt(111))/2
Find the zeros of 0=x^3+21x-90
The zeros of 0=x^3+21x-90 are x=3,x=-3/2+i(sqrt(111))/2 ,x=-3/2-i(sqrt(111))/2