Solve sqrt{x}=x/7

$$\sqrt { x } = \frac { x } { 7 }$$

Solve for x

$$x=0$$

$$x=49$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x}\right)^{2}=\left(\frac{x}{7}\right)^{2}$$

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

$$x=\left(\frac{x}{7}\right)^{2}$$

To raise \frac{x}{7} to a power, raise both numerator and denominator to the power and then divide.

$$x=\frac{x^{2}}{7^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$x=\frac{x^{2}}{49}$$

Subtract \frac{x^{2}}{49} from both sides.

$$x-\frac{x^{2}}{49}=0$$

Multiply both sides of the equation by 49.

$$49x-x^{2}=0$$

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.

$$-x^{2}+49x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 49 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-49±\sqrt{49^{2}}}{2\left(-1\right)}$$

Take the square root of 49^{2}.

$$x=\frac{-49±49}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-49±49}{-2}$$

Now solve the equation x=\frac{-49±49}{-2} when ± is plus. Add -49 to 49.

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

Divide 0 by -2.

$$x=0$$

Now solve the equation x=\frac{-49±49}{-2} when ± is minus. Subtract 49 from -49.

$$x=-\frac{98}{-2}$$

Divide -98 by -2.

$$x=49$$

The equation is now solved.

$$x=0 x=49$$

Substitute 0 for x in the equation \sqrt{x}=\frac{x}{7}.

$$\sqrt{0}=\frac{0}{7}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 49 for x in the equation \sqrt{x}=\frac{x}{7}.

$$\sqrt{49}=\frac{49}{7}$$

Simplify. The value x=49 satisfies the equation.

$$7=7$$

List all solutions of \sqrt{x}=\frac{x}{7}.

$$x=0 x=49$$