What are the solutions to the equation 4x+8=2x^3 ?

The solutions to the equation 4x+8=2x^3 are x=2,x=-1+i,x=-1-i

Find the zeros of 4x+8=2x^3

The zeros of 4x+8=2x^3 are x=2,x=-1+i,x=-1-i

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4 x + 8 = 2 x^{3}

x = 2, x = - 1 + i, x = - 1 - i

Solution steps

4 x + 8 = 2 x^{3}

Switch sides

2 x^{3} = 4 x + 8

Move

8

to the left side

2 x^{3} - 8 = 4 x

Move

4 x

to the left side

2 x^{3} - 8 - 4 x = 0

Write in the standard form

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

2 x^{3} - 4 x - 8 = 0

Factor

2 x^{3} - 4 x - 8 : 2 (x - 2) (x^{2} + 2 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 2 = 0 : x = - 1 + i, x = - 1 - i

The solutions are

x = 2, x = - 1 + i, x = - 1 - i

x^{4} - 2 x^{3} - 10 x^{2} + 18 x + 9 = 0

4 (\frac{x ^{3}}{4})^{3} - 16 x = 0

x^{5} = - 243

0 = x^{5} - 2.2 x^{4} - 6.61 x^{3} + 8.602 x^{2}

x^{3} + 5 x^{2} - 36 x = 0

What are the solutions to the equation 4x+8=2x^3 ?
The solutions to the equation 4x+8=2x^3 are x=2,x=-1+i,x=-1-i
Find the zeros of 4x+8=2x^3
The zeros of 4x+8=2x^3 are x=2,x=-1+i,x=-1-i