Solve 7x-3sqrt{x}=0

$$7 x - 3 \sqrt { x } = 0$$

Solve for x

$$x=0$$

$$x=\frac{9}{49}\approx 0.183673469$$

Solution Steps

Subtract 7x from both sides of the equation.

$$-3\sqrt{x}=-7x$$

Square both sides of the equation.

$$\left(-3\sqrt{x}\right)^{2}=\left(-7x\right)^{2}$$

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

$$\left(-3\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-7x\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$9\left(\sqrt{x}\right)^{2}=\left(-7x\right)^{2}$$

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

$$9x=\left(-7x\right)^{2}$$

Expand \left(-7x\right)^{2}.

$$9x=\left(-7\right)^{2}x^{2}$$

Calculate -7 to the power of 2 and get 49.

$$9x=49x^{2}$$

Subtract 49x^{2} from both sides.

$$9x-49x^{2}=0$$

Factor out x.

$$x\left(9-49x\right)=0$$

To find equation solutions, solve x=0 and 9-49x=0.

$$x=0 x=\frac{9}{49}$$

Substitute 0 for x in the equation 7x-3\sqrt{x}=0.

$$7\times 0-3\sqrt{0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{9}{49} for x in the equation 7x-3\sqrt{x}=0.

$$7\times \frac{9}{49}-3\sqrt{\frac{9}{49}}=0$$

Simplify. The value x=\frac{9}{49} satisfies the equation.

$$0=0$$

List all solutions of -3\sqrt{x}=-7x.

$$x=0 x=\frac{9}{49}$$