Solve sqrt{3}(100-sqrt{3}x)=x

$$\sqrt { 3 } ( 100 - \sqrt { 3 } x ) = x$$

Solve for x

$$x=25\sqrt{3}\approx 43.301270189$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\sqrt{3}\left(100-\sqrt{3}x\right)-x=0$$

Use the distributive property to multiply \sqrt{3} by 100-\sqrt{3}x.

$$100\sqrt{3}-x\left(\sqrt{3}\right)^{2}-x=0$$

The square of \sqrt{3} is 3.

$$100\sqrt{3}-x\times 3-x=0$$

Multiply -1 and 3 to get -3.

$$100\sqrt{3}-3x-x=0$$

Combine -3x and -x to get -4x.

$$100\sqrt{3}-4x=0$$

Subtract 100\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$-4x=-100\sqrt{3}$$

Divide both sides by -4.

$$\frac{-4x}{-4}=-\frac{100\sqrt{3}}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=-\frac{100\sqrt{3}}{-4}$$

Divide -100\sqrt{3} by -4.

$$x=25\sqrt{3}$$