Solve 44633466/5134334344334*sqrt{58/99999}+663434sqrt{5/8/frac{5{9}}}x=9

$$\frac{ 44633466 }{ 5134334344334 } \times \sqrt{ \frac{ 58 }{ 99999 } } +663434 \sqrt{ \frac{ \frac{ 5 }{ 8 } }{ \frac{ 5 }{ 9 } } } x=9$$

Solve for x

$$x=\frac{3\sqrt{2}}{331717}-\frac{4959274\sqrt{322219}}{9461827523553247131029}\approx 0.00001279$$

Steps for Solving Linear Equation

Reduce the fraction \frac{44633466}{5134334344334} to lowest terms by extracting and canceling out 2.

$$\frac{22316733}{2567167172167}\sqrt{\frac{58}{99999}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Rewrite the square root of the division \sqrt{\frac{58}{99999}} as the division of square roots \frac{\sqrt{58}}{\sqrt{99999}}.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}}{\sqrt{99999}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Factor 99999=3^{2}\times 11111. Rewrite the square root of the product \sqrt{3^{2}\times 11111} as the product of square roots \sqrt{3^{2}}\sqrt{11111}. Take the square root of 3^{2}.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}}{3\sqrt{11111}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Rationalize the denominator of \frac{\sqrt{58}}{3\sqrt{11111}} by multiplying numerator and denominator by \sqrt{11111}.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}\sqrt{11111}}{3\left(\sqrt{11111}\right)^{2}}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

The square of \sqrt{11111} is 11111.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{58}\sqrt{11111}}{3\times 11111}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

To multiply \sqrt{58} and \sqrt{11111}, multiply the numbers under the square root.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{644438}}{3\times 11111}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Multiply 3 and 11111 to get 33333.

$$\frac{22316733}{2567167172167}\times \frac{\sqrt{644438}}{33333}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Multiply \frac{22316733}{2567167172167} times \frac{\sqrt{644438}}{33333} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22316733\sqrt{644438}}{2567167172167\times 33333}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Cancel out 3 in both numerator and denominator.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{\frac{5}{8}}{\frac{5}{9}}}x=9$$

Divide \frac{5}{8} by \frac{5}{9} by multiplying \frac{5}{8} by the reciprocal of \frac{5}{9}.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{5}{8}\times \frac{9}{5}}x=9$$

Multiply \frac{5}{8} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{5\times 9}{8\times 5}}x=9$$

Cancel out 5 in both numerator and denominator.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\sqrt{\frac{9}{8}}x=9$$

Rewrite the square root of the division \sqrt{\frac{9}{8}} as the division of square roots \frac{\sqrt{9}}{\sqrt{8}}.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{\sqrt{9}}{\sqrt{8}}x=9$$

Calculate the square root of 9 and get 3.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3}{\sqrt{8}}x=9$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3}{2\sqrt{2}}x=9$$

Rationalize the denominator of \frac{3}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}x=9$$

The square of \sqrt{2} is 2.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{2\times 2}x=9$$

Multiply 2 and 2 to get 4.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+663434\times \frac{3\sqrt{2}}{4}x=9$$

Express 663434\times \frac{3\sqrt{2}}{4} as a single fraction.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+\frac{663434\times 3\sqrt{2}}{4}x=9$$

Express \frac{663434\times 3\sqrt{2}}{4}x as a single fraction.

$$\frac{7438911\sqrt{644438}}{11111\times 2567167172167}+\frac{663434\times 3\sqrt{2}x}{4}=9$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11111\times 2567167172167 and 4 is 114095177799790148. Multiply \frac{7438911\sqrt{644438}}{11111\times 2567167172167} times \frac{4}{4}. Multiply \frac{663434\times 3\sqrt{2}x}{4} times \frac{28523794449947537}{28523794449947537}.

$$\frac{4\times 7438911\sqrt{644438}}{114095177799790148}+\frac{28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148}=9$$

Since \frac{4\times 7438911\sqrt{644438}}{114095177799790148} and \frac{28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148} have the same denominator, add them by adding their numerators.

$$\frac{4\times 7438911\sqrt{644438}+28523794449947537\times 663434\times 3\sqrt{2}x}{114095177799790148}=9$$

Do the multiplications in 4\times 7438911\sqrt{644438}+28523794449947537\times 663434\times 3\sqrt{2}x.

$$\frac{29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x}{114095177799790148}=9$$

Multiply both sides by 114095177799790148.

$$29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x=9\times 114095177799790148$$

Multiply 9 and 114095177799790148 to get 1026856600198111332.

$$29755644\sqrt{644438}+56770965141319482786174\sqrt{2}x=1026856600198111332$$

Subtract 29755644\sqrt{644438} from both sides.

$$56770965141319482786174\sqrt{2}x=1026856600198111332-29755644\sqrt{644438}$$

Divide both sides by 56770965141319482786174\sqrt{2}.

$$\frac{56770965141319482786174\sqrt{2}x}{56770965141319482786174\sqrt{2}}=\frac{1026856600198111332-29755644\sqrt{644438}}{56770965141319482786174\sqrt{2}}$$

Dividing by 56770965141319482786174\sqrt{2} undoes the multiplication by 56770965141319482786174\sqrt{2}.

$$x=\frac{1026856600198111332-29755644\sqrt{644438}}{56770965141319482786174\sqrt{2}}$$

Divide 1026856600198111332-29755644\sqrt{644438} by 56770965141319482786174\sqrt{2}.

$$x=\frac{3\sqrt{2}}{331717}-\frac{4959274\sqrt{322219}}{9461827523553247131029}$$