Solve 8x=458sqrt{5x*218*x*14}

$$8x=458 \sqrt{ 5x \times 218 \times x \times 14 }$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(8x\right)^{2}=\left(458\sqrt{5x\times 218x\times 14}\right)^{2}$$

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

$$\left(8x\right)^{2}=\left(458\sqrt{5x^{2}\times 218\times 14}\right)^{2}$$

Expand \left(8x\right)^{2}.

$$8^{2}x^{2}=\left(458\sqrt{5x^{2}\times 218\times 14}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64x^{2}=\left(458\sqrt{5x^{2}\times 218\times 14}\right)^{2}$$

Multiply 5 and 218 to get 1090.

$$64x^{2}=\left(458\sqrt{1090x^{2}\times 14}\right)^{2}$$

Multiply 1090 and 14 to get 15260.

$$64x^{2}=\left(458\sqrt{15260x^{2}}\right)^{2}$$

Expand \left(458\sqrt{15260x^{2}}\right)^{2}.

$$64x^{2}=458^{2}\left(\sqrt{15260x^{2}}\right)^{2}$$

Calculate 458 to the power of 2 and get 209764.

$$64x^{2}=209764\left(\sqrt{15260x^{2}}\right)^{2}$$

Calculate \sqrt{15260x^{2}} to the power of 2 and get 15260x^{2}.

$$64x^{2}=209764\times 15260x^{2}$$

Multiply 209764 and 15260 to get 3200998640.

$$64x^{2}=3200998640x^{2}$$

Subtract 3200998640x^{2} from both sides.

$$64x^{2}-3200998640x^{2}=0$$

Combine 64x^{2} and -3200998640x^{2} to get -3200998576x^{2}.

$$-3200998576x^{2}=0$$

Divide both sides by -3200998576. Zero divided by any non-zero number 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 8x=458\sqrt{5x\times 218x\times 14}.

$$8\times 0=458\sqrt{5\times 0\times 218\times 0\times 14}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation 8x=458\sqrt{15260x^{2}} has a unique solution.

$$x=0$$