Solve 1(x)=10sqrt{300x-2x^2}

$$1 ( x ) = 10 \sqrt { 300 x - 2 x ^ { 2 } }$$

Solve for x

$$x = \frac{10000}{67} = 149\frac{17}{67} \approx 149.253731343$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(1x\right)^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

Expand \left(1x\right)^{2}.

$$1^{2}x^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1x^{2}=\left(10\sqrt{300x-2x^{2}}\right)^{2}$$

Expand \left(10\sqrt{300x-2x^{2}}\right)^{2}.

$$1x^{2}=10^{2}\left(\sqrt{300x-2x^{2}}\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$1x^{2}=100\left(\sqrt{300x-2x^{2}}\right)^{2}$$

Calculate \sqrt{300x-2x^{2}} to the power of 2 and get 300x-2x^{2}.

$$1x^{2}=100\left(300x-2x^{2}\right)$$

Use the distributive property to multiply 100 by 300x-2x^{2}.

$$1x^{2}=30000x-200x^{2}$$

Reorder the terms.

$$x^{2}=-200x^{2}+30000x$$

Add 200x^{2} to both sides.

$$x^{2}+200x^{2}=30000x$$

Combine x^{2} and 200x^{2} to get 201x^{2}.

$$201x^{2}=30000x$$

Subtract 30000x from both sides.

$$201x^{2}-30000x=0$$

Factor out x.

$$x\left(201x-30000\right)=0$$

To find equation solutions, solve x=0 and 201x-30000=0.

$$x=0 x=\frac{10000}{67}$$

Substitute 0 for x in the equation 1x=10\sqrt{300x-2x^{2}}.

$$1\times 0=10\sqrt{300\times 0-2\times 0^{2}}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{10000}{67} for x in the equation 1x=10\sqrt{300x-2x^{2}}.

$$1\times \frac{10000}{67}=10\sqrt{300\times \frac{10000}{67}-2\times \left(\frac{10000}{67}\right)^{2}}$$

Simplify. The value x=\frac{10000}{67} satisfies the equation.

$$\frac{10000}{67}=\frac{10000}{67}$$

List all solutions of x=10\sqrt{300x-2x^{2}}.

$$x=0 x=\frac{10000}{67}$$