Solve x=sqrt{x}*x+x/x

$$x = \sqrt { x } \times \frac { x + x } { x }$$

Solve for x

$$x=4$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{x}\times \frac{x+x}{x}\right)^{2}$$

Combine x and x to get 2x.

$$x^{2}=\left(\sqrt{x}\times \frac{2x}{x}\right)^{2}$$

Cancel out x in both numerator and denominator.

$$x^{2}=\left(\sqrt{x}\times 2\right)^{2}$$

Expand \left(\sqrt{x}\times 2\right)^{2}.

$$x^{2}=\left(\sqrt{x}\right)^{2}\times 2^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$x^{2}=x\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=x\times 4$$

Subtract x\times 4 from both sides.

$$x^{2}-x\times 4=0$$

Multiply -1 and 4 to get -4.

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

Factor out x.

$$x\left(x-4\right)=0$$

To find equation solutions, solve x=0 and x-4=0.

$$x=0 x=4$$

Substitute 0 for x in the equation x=\sqrt{x}\times \frac{x+x}{x}. The expression is undefined.

$$0=\sqrt{0}\times \frac{0+0}{0}$$

Substitute 4 for x in the equation x=\sqrt{x}\times \frac{x+x}{x}.

$$4=\sqrt{4}\times \frac{4+4}{4}$$

Simplify. The value x=4 satisfies the equation.

$$4=4$$

Equation x=\frac{x+x}{x}\sqrt{x} has a unique solution.

$$x=4$$