What are the solutions to the equation x^3+8x-16=3x+2x^2-6 ?

The solutions to the equation x^3+8x-16=3x+2x^2-6 are x=2,x=sqrt(5)i,x=-sqrt(5)i

Find the zeros of x^3+8x-16=3x+2x^2-6

The zeros of x^3+8x-16=3x+2x^2-6 are x=2,x=sqrt(5)i,x=-sqrt(5)i

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x^{3} + 8 x - 16 = 3 x + 2 x^{2} - 6

x = 2, x = 5 i, x = - 5 i

Solution steps

x^{3} + 8 x - 16 = 3 x + 2 x^{2} - 6

Move

6

to the left side

x^{3} + 8 x - 10 = 3 x + 2 x^{2}

Move

2 x^{2}

to the left side

x^{3} + 8 x - 10 - 2 x^{2} = 3 x

Move

3 x

to the left side

x^{3} - 2 x^{2} + 5 x - 10 = 0

Factor

x^{3} - 2 x^{2} + 5 x - 10 : (x - 2) (x^{2} + 5)

(x - 2) (x^{2} + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 5 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 5 = 0 : x = 5 i, x = - 5 i

The solutions are

x = 2, x = 5 i, x = - 5 i

4 x^{5} + 5 x^{4} - 20 x^{3} - 25 x^{2} + 16 x + 20 = 0

4.19 x^{3} - 402.12 x + 104 = 0

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

2 x^{3} + 2 = 0

2 x^{3} - 5 x^{2} + 40 x - 100 = 0

What are the solutions to the equation x^3+8x-16=3x+2x^2-6 ?
The solutions to the equation x^3+8x-16=3x+2x^2-6 are x=2,x=sqrt(5)i,x=-sqrt(5)i
Find the zeros of x^3+8x-16=3x+2x^2-6
The zeros of x^3+8x-16=3x+2x^2-6 are x=2,x=sqrt(5)i,x=-sqrt(5)i