What are the solutions to the equation x^3-4+(4)x=x ?

The solutions to the equation x^3-4+(4)x=x are x=1,x=-1/2+i(sqrt(15))/2 ,x=-1/2-i(sqrt(15))/2

Find the zeros of x^3-4+(4)x=x

The zeros of x^3-4+(4)x=x are x=1,x=-1/2+i(sqrt(15))/2 ,x=-1/2-i(sqrt(15))/2

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x^{3} - 4 + (4) x = x

x = 1, x = - \frac{1}{2} + i \frac{15}{2}, x = - \frac{1}{2} - i \frac{15}{2}

Solution steps

x^{3} - 4 + (4) x = x

Refine

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

Move

x

to the left side

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

Write in the standard form

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

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

Factor

x^{3} + 3 x - 4 : (x - 1) (x^{2} + x + 4)

(x - 1) (x^{2} + x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x + 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 4 = 0 : x = - \frac{1}{2} + i \frac{15}{2}, x = - \frac{1}{2} - i \frac{15}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{15}{2}, x = - \frac{1}{2} - i \frac{15}{2}

m^{3} - 3 m^{2} + 3 m + 1 = 0

x^{3} - 10 x^{2} + 25 x - 63 = 0

6 x^{4} + 7 x^{3} - 22 x^{2} - 28 x - 8 = 0

4 x^{4} + 13 x + 9 = 0

(x - 1)^{3} = 27

What are the solutions to the equation x^3-4+(4)x=x ?
The solutions to the equation x^3-4+(4)x=x are x=1,x=-1/2+i(sqrt(15))/2 ,x=-1/2-i(sqrt(15))/2
Find the zeros of x^3-4+(4)x=x
The zeros of x^3-4+(4)x=x are x=1,x=-1/2+i(sqrt(15))/2 ,x=-1/2-i(sqrt(15))/2