Solve x=42sqrt{41%x*0.125*x}

$$x=42 \sqrt{ 41 \% x \times 0.125 \times x }$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(42\sqrt{\frac{41}{100}x\times 0.125x}\right)^{2}$$

Multiply x and x to get x^{2}.

$$x^{2}=\left(42\sqrt{\frac{41}{100}x^{2}\times 0.125}\right)^{2}$$

Convert decimal number 0.125 to fraction \frac{125}{1000}. Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$x^{2}=\left(42\sqrt{\frac{41}{100}x^{2}\times \frac{1}{8}}\right)^{2}$$

Multiply \frac{41}{100} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}=\left(42\sqrt{\frac{41\times 1}{100\times 8}x^{2}}\right)^{2}$$

Do the multiplications in the fraction \frac{41\times 1}{100\times 8}.

$$x^{2}=\left(42\sqrt{\frac{41}{800}x^{2}}\right)^{2}$$

Expand \left(42\sqrt{\frac{41}{800}x^{2}}\right)^{2}.

$$x^{2}=42^{2}\left(\sqrt{\frac{41}{800}x^{2}}\right)^{2}$$

Calculate 42 to the power of 2 and get 1764.

$$x^{2}=1764\left(\sqrt{\frac{41}{800}x^{2}}\right)^{2}$$

Calculate \sqrt{\frac{41}{800}x^{2}} to the power of 2 and get \frac{41}{800}x^{2}.

$$x^{2}=1764\times \frac{41}{800}x^{2}$$

Express 1764\times \frac{41}{800} as a single fraction.

$$x^{2}=\frac{1764\times 41}{800}x^{2}$$

Multiply 1764 and 41 to get 72324.

$$x^{2}=\frac{72324}{800}x^{2}$$

Reduce the fraction \frac{72324}{800} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{18081}{200}x^{2}$$

Subtract \frac{18081}{200}x^{2} from both sides.

$$x^{2}-\frac{18081}{200}x^{2}=0$$

Combine x^{2} and -\frac{18081}{200}x^{2} to get -\frac{17881}{200}x^{2}.

$$-\frac{17881}{200}x^{2}=0$$

Multiply both sides by -\frac{200}{17881}, the reciprocal of -\frac{17881}{200}. Anything times zero gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Substitute 0 for x in the equation x=42\sqrt{\frac{41}{100}x\times 0.125x}.

$$0=42\sqrt{\frac{41}{100}\times 0\times 0.125\times 0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation x=42\sqrt{\frac{5.125x^{2}}{100}} has a unique solution.

$$x=0$$