Solve (1+2)sqrt{x^2}=x

$$(1+2) \sqrt{ { x }^{ 2 } } =x$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(\left(1+2\right)\sqrt{x^{2}}\right)^{2}=x^{2}$$

Add 1 and 2 to get 3.

$$\left(3\sqrt{x^{2}}\right)^{2}=x^{2}$$

Expand \left(3\sqrt{x^{2}}\right)^{2}.

$$3^{2}\left(\sqrt{x^{2}}\right)^{2}=x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{x^{2}}\right)^{2}=x^{2}$$

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

$$9x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$9x^{2}-x^{2}=0$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}=0$$

Divide both sides by 8. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Substitute 0 for x in the equation \left(1+2\right)\sqrt{x^{2}}=x.

$$\left(1+2\right)\sqrt{0^{2}}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation 3\sqrt{x^{2}}=x has a unique solution.

$$x=0$$