Solve sqrt{x}*5=4x

$$\sqrt { x } \cdot 5 = 4 x$$

Solve for x

$$x=0$$

$$x = \frac{25}{16} = 1\frac{9}{16} = 1.5625$$

Solution Steps

Square both sides of the equation.

$$\left(5\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

Expand \left(5\sqrt{x}\right)^{2}.

$$5^{2}\left(\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

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

$$25x=\left(4x\right)^{2}$$

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

$$25x=4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$25x=16x^{2}$$

Subtract 16x^{2} from both sides.

$$25x-16x^{2}=0$$

Factor out x.

$$x\left(25-16x\right)=0$$

To find equation solutions, solve x=0 and 25-16x=0.

$$x=0 x=\frac{25}{16}$$

Substitute 0 for x in the equation 5\sqrt{x}=4x.

$$5\sqrt{0}=4\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{25}{16} for x in the equation 5\sqrt{x}=4x.

$$5\sqrt{\frac{25}{16}}=4\times \frac{25}{16}$$

Simplify. The value x=\frac{25}{16} satisfies the equation.

$$\frac{25}{4}=\frac{25}{4}$$

List all solutions of 5\sqrt{x}=4x.

$$x=0 x=\frac{25}{16}$$