Solve sqrt{x}=x/3

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

Solve for x

$$x=0$$

$$x=9$$

Solution Steps

Square both sides of the equation.

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

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

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

To raise \frac{x}{3} to a power, raise both numerator and denominator to the power and then divide.

$$x=\frac{x^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

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

Subtract \frac{x^{2}}{9} from both sides.

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

Multiply both sides of the equation by 9.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 9 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}}}{2\left(-1\right)}$$

Take the square root of 9^{2}.

$$x=\frac{-9±9}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-9±9}{-2}$$

Now solve the equation x=\frac{-9±9}{-2} when ± is plus. Add -9 to 9.

$$x=\frac{0}{-2}$$

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-9±9}{-2} when ± is minus. Subtract 9 from -9.

$$x=-\frac{18}{-2}$$

Divide -18 by -2.

$$x=9$$

The equation is now solved.

$$x=0 x=9$$

Substitute 0 for x in the equation \sqrt{x}=\frac{x}{3}.

$$\sqrt{0}=\frac{0}{3}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 9 for x in the equation \sqrt{x}=\frac{x}{3}.

$$\sqrt{9}=\frac{9}{3}$$

Simplify. The value x=9 satisfies the equation.

$$3=3$$

List all solutions of \sqrt{x}=\frac{x}{3}.

$$x=0 x=9$$