Solve xdx=quadd(4-2x^2)

$$x d x = \quad d ( 4 - 2 x ^ { 2 } )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=-\frac{2\sqrt{3}}{3}\text{ or }x=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=d\left(4-2x^{2}\right)$$

Use the distributive property to multiply d by 4-2x^{2}.

$$x^{2}d=4d-2dx^{2}$$

Subtract 4d from both sides.

$$x^{2}d-4d=-2dx^{2}$$

Add 2dx^{2} to both sides.

$$x^{2}d-4d+2dx^{2}=0$$

Combine x^{2}d and 2dx^{2} to get 3x^{2}d.

$$3x^{2}d-4d=0$$

Combine all terms containing d.

$$\left(3x^{2}-4\right)d=0$$

Divide 0 by 3x^{2}-4.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&|x|=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$x^{2}d=d\left(4-2x^{2}\right)$$

Use the distributive property to multiply d by 4-2x^{2}.

$$x^{2}d=4d-2dx^{2}$$

Subtract 4d from both sides.

$$x^{2}d-4d=-2dx^{2}$$

Add 2dx^{2} to both sides.

$$x^{2}d-4d+2dx^{2}=0$$

Combine x^{2}d and 2dx^{2} to get 3x^{2}d.

$$3x^{2}d-4d=0$$

Combine all terms containing d.

$$\left(3x^{2}-4\right)d=0$$

Divide 0 by 3x^{2}-4.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{2\sqrt{3}}{3}\text{; }x=\frac{2\sqrt{3}}{3}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{2\sqrt{3}}{3}\text{; }x=-\frac{2\sqrt{3}}{3}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$