What are the solutions to the equation x^4+16=2x^3+8x ?

The solutions to the equation x^4+16=2x^3+8x are x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of x^4+16=2x^3+8x

The zeros of x^4+16=2x^3+8x are x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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x^{4} + 16 = 2 x^{3} + 8 x

x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

x^{4} + 16 = 2 x^{3} + 8 x

Move

8 x

to the left side

x^{4} + 16 - 8 x = 2 x^{3}

Move

2 x^{3}

to the left side

x^{4} + 16 - 8 x - 2 x^{3} = 0

Write in the standard form

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

x^{4} - 2 x^{3} - 8 x + 16 = 0

Factor

x^{4} - 2 x^{3} - 8 x + 16 : (x - 2)^{2} (x^{2} + 2 x + 4)

(x - 2)^{2} (x^{2} + 2 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 2 x + 4 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 4 = 0 : x = - 1 + 3 i, x = - 1 - 3 i

The solutions are

x = 2, x = - 1 + 3 i, x = - 1 - 3 i

4 x^{3} + 8 x^{2} - 9 x = 18

x^{2} (2 x^{2} + 6) = 8

1331 x^{3} - 216 = 0

3 x^{3} - 15 x^{2} - 18 x = 0

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

What are the solutions to the equation x^4+16=2x^3+8x ?
The solutions to the equation x^4+16=2x^3+8x are x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of x^4+16=2x^3+8x
The zeros of x^4+16=2x^3+8x are x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i