What are the solutions to the equation -24x-24=x^3+8x^2 ?

The solutions to the equation -24x-24=x^3+8x^2 are x=-2,x=-3+sqrt(3)i,x=-3-sqrt(3)i

Find the zeros of -24x-24=x^3+8x^2

The zeros of -24x-24=x^3+8x^2 are x=-2,x=-3+sqrt(3)i,x=-3-sqrt(3)i

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- 24 x - 24 = x^{3} + 8 x^{2}

x = - 2, x = - 3 + 3 i, x = - 3 - 3 i

Solution steps

- 24 x - 24 = x^{3} + 8 x^{2}

Switch sides

x^{3} + 8 x^{2} = - 24 x - 24

Move

24

to the left side

x^{3} + 8 x^{2} + 24 = - 24 x

Move

24 x

to the left side

x^{3} + 8 x^{2} + 24 + 24 x = 0

Write in the standard form

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

x^{3} + 8 x^{2} + 24 x + 24 = 0

Factor

x^{3} + 8 x^{2} + 24 x + 24 : (x + 2) (x^{2} + 6 x + 12)

(x + 2) (x^{2} + 6 x + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x^{2} + 6 x + 12 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x^{2} + 6 x + 12 = 0 : x = - 3 + 3 i, x = - 3 - 3 i

The solutions are

x = - 2, x = - 3 + 3 i, x = - 3 - 3 i

4 x (5 x^{2} - 3) = 0

20 x = x^{2} (x) + 36 x - 2 x (x) (x)

y, y^{2} - y^{4} = x

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

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

What are the solutions to the equation -24x-24=x^3+8x^2 ?
The solutions to the equation -24x-24=x^3+8x^2 are x=-2,x=-3+sqrt(3)i,x=-3-sqrt(3)i
Find the zeros of -24x-24=x^3+8x^2
The zeros of -24x-24=x^3+8x^2 are x=-2,x=-3+sqrt(3)i,x=-3-sqrt(3)i