Solve 5562155*52155/5552x=222*sqrt{2x}

$$5562155 \times \frac{ 52155 }{ 5552 } x=222 \times \sqrt{ 2x }$$

Solve for x

$$x=\frac{337592158208}{9350515711890482855625}\approx 3.610412181 \cdot 10^{-11}$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(5562155\times \frac{52155}{5552}x\right)^{2}=\left(222\sqrt{2x}\right)^{2}$$

Express 5562155\times \frac{52155}{5552} as a single fraction.

$$\left(\frac{5562155\times 52155}{5552}x\right)^{2}=\left(222\sqrt{2x}\right)^{2}$$

Multiply 5562155 and 52155 to get 290094194025.

$$\left(\frac{290094194025}{5552}x\right)^{2}=\left(222\sqrt{2x}\right)^{2}$$

Expand \left(\frac{290094194025}{5552}x\right)^{2}.

$$\left(\frac{290094194025}{5552}\right)^{2}x^{2}=\left(222\sqrt{2x}\right)^{2}$$

Calculate \frac{290094194025}{5552} to the power of 2 and get \frac{84154641407014345700625}{30824704}.

$$\frac{84154641407014345700625}{30824704}x^{2}=\left(222\sqrt{2x}\right)^{2}$$

Expand \left(222\sqrt{2x}\right)^{2}.

$$\frac{84154641407014345700625}{30824704}x^{2}=222^{2}\left(\sqrt{2x}\right)^{2}$$

Calculate 222 to the power of 2 and get 49284.

$$\frac{84154641407014345700625}{30824704}x^{2}=49284\left(\sqrt{2x}\right)^{2}$$

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

$$\frac{84154641407014345700625}{30824704}x^{2}=49284\times 2x$$

Multiply 49284 and 2 to get 98568.

$$\frac{84154641407014345700625}{30824704}x^{2}=98568x$$

Subtract 98568x from both sides.

$$\frac{84154641407014345700625}{30824704}x^{2}-98568x=0$$

Factor out x.

$$x\left(\frac{84154641407014345700625}{30824704}x-98568\right)=0$$

To find equation solutions, solve x=0 and \frac{84154641407014345700625x}{30824704}-98568=0.

$$x=0 x=\frac{337592158208}{9350515711890482855625}$$

Substitute 0 for x in the equation 5562155\times \frac{52155}{5552}x=222\sqrt{2x}.

$$5562155\times \frac{52155}{5552}\times 0=222\sqrt{2\times 0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{337592158208}{9350515711890482855625} for x in the equation 5562155\times \frac{52155}{5552}x=222\sqrt{2x}.

$$5562155\times \frac{52155}{5552}\times \frac{337592158208}{9350515711890482855625}=222\sqrt{2\times \frac{337592158208}{9350515711890482855625}}$$

Simplify. The value x=\frac{337592158208}{9350515711890482855625} satisfies the equation.

$$\frac{60805504}{32232688225}=\frac{60805504}{32232688225}$$

List all solutions of \frac{290094194025}{5552}x=222\sqrt{2x}.

$$x=0 x=\frac{337592158208}{9350515711890482855625}$$