What are the solutions to the equation x(x+ax)dx+ax(ax-x)(adx+xda)=0 ?

The solutions to the equation x(x+ax)dx+ax(ax-x)(adx+xda)=0 are x=0;\quad d\ne 0,a\ne-0.44061…

Find the zeros of x(x+ax)dx+ax(ax-x)(adx+xda)=0

The zeros of x(x+ax)dx+ax(ax-x)(adx+xda)=0 are x=0;\quad d\ne 0,a\ne-0.44061…

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x (x + a x) d x + a x (a x - x) (a d x + x d a) = 0

x = 0; d \neq = 0, a \neq = - 0.44061 \dots

Solution steps

x (x + a x) d x + a x (a x - x) (a d x + x d a) = 0

Factor

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

x^{3} d (1 + a + 2 a^{3} - 2 a^{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0

The solution is

x = 0; d \neq = 0, a \neq = - 0.44061 \dots

z^{4} + 2 i = 6 + 3 i

z^{4} = 9 + 8 z^{2}

(1 + \frac{x}{12})^{12} = 1.08

u^{3} + 8 = (u + 2)

- 6 + w^{3} = - 9

What are the solutions to the equation x(x+ax)dx+ax(ax-x)(adx+xda)=0 ?
The solutions to the equation x(x+ax)dx+ax(ax-x)(adx+xda)=0 are x=0;\quad d\ne 0,a\ne-0.44061…
Find the zeros of x(x+ax)dx+ax(ax-x)(adx+xda)=0
The zeros of x(x+ax)dx+ax(ax-x)(adx+xda)=0 are x=0;\quad d\ne 0,a\ne-0.44061…