Solve 4x=3sqrt{x}

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

Solve for x

$$x=0$$

$$x=\frac{9}{16}=0.5625$$

Solution Steps

Square both sides of the equation.

$$\left(4x\right)^{2}=\left(3\sqrt{x}\right)^{2}$$

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}=\left(3\sqrt{x}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=\left(3\sqrt{x}\right)^{2}$$

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

$$16x^{2}=3^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}=9\left(\sqrt{x}\right)^{2}$$

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

$$16x^{2}=9x$$

Subtract 9x from both sides.

$$16x^{2}-9x=0$$

Factor out x.

$$x\left(16x-9\right)=0$$

To find equation solutions, solve x=0 and 16x-9=0.

$$x=0 x=\frac{9}{16}$$

Substitute 0 for x in the equation 4x=3\sqrt{x}.

$$4\times 0=3\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{9}{16} for x in the equation 4x=3\sqrt{x}.

$$4\times \frac{9}{16}=3\sqrt{\frac{9}{16}}$$

Simplify. The value x=\frac{9}{16} satisfies the equation.

$$\frac{9}{4}=\frac{9}{4}$$

List all solutions of 4x=3\sqrt{x}.

$$x=0 x=\frac{9}{16}$$