Solve 0.1=2y(1-0.1/1+0.1-x/sqrt{9.96*10^6})-1

$$0.1=2y( \frac{ 1-0.1 }{ 1+0.1 } - \frac{ x }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x=\frac{10\sqrt{249}\left(180y-121\right)}{11y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 0.1 from 1 to get 0.9.

$$0.1=2y\left(\frac{0.9}{1+0.1}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Add 1 and 0.1 to get 1.1.

$$0.1=2y\left(\frac{0.9}{1.1}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Expand \frac{0.9}{1.1} by multiplying both numerator and the denominator by 10.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9960000}}\right)-1$$

Factor 9960000=200^{2}\times 249. Rewrite the square root of the product \sqrt{200^{2}\times 249} as the product of square roots \sqrt{200^{2}}\sqrt{249}. Take the square root of 200^{2}.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{x}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{49800}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11 and 49800 is 547800. Multiply \frac{9}{11} times \frac{49800}{49800}. Multiply \frac{x\sqrt{249}}{49800} times \frac{11}{11}.

$$0.1=2y\left(\frac{9\times 49800}{547800}-\frac{11x\sqrt{249}}{547800}\right)-1$$

Since \frac{9\times 49800}{547800} and \frac{11x\sqrt{249}}{547800} have the same denominator, subtract them by subtracting their numerators.

$$0.1=2y\times \frac{9\times 49800-11x\sqrt{249}}{547800}-1$$

Do the multiplications in 9\times 49800-11x\sqrt{249}.

$$0.1=2y\times \frac{448200-11x\sqrt{249}}{547800}-1$$

Cancel out 547800, the greatest common factor in 2 and 547800.

$$0.1=\frac{448200-11x\sqrt{249}}{273900}y-1$$

Express \frac{448200-11x\sqrt{249}}{273900}y as a single fraction.

$$0.1=\frac{\left(448200-11x\sqrt{249}\right)y}{273900}-1$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\left(448200-11x\sqrt{249}\right)y}{273900}-1=0.1$$

Use the distributive property to multiply 448200-11x\sqrt{249} by y.

$$\frac{448200y-11x\sqrt{249}y}{273900}-1=0.1$$

Add 1 to both sides.

$$\frac{448200y-11x\sqrt{249}y}{273900}=0.1+1$$

Add 0.1 and 1 to get 1.1.

$$\frac{448200y-11x\sqrt{249}y}{273900}=1.1$$

Multiply both sides by 273900.

$$448200y-11x\sqrt{249}y=1.1\times 273900$$

Multiply 1.1 and 273900 to get 301290.

$$448200y-11x\sqrt{249}y=301290$$

Subtract 448200y from both sides.

$$-11x\sqrt{249}y=301290-448200y$$

The equation is in standard form.

$$\left(-11\sqrt{249}y\right)x=301290-448200y$$

Divide both sides by -11\sqrt{249}y.

$$\frac{\left(-11\sqrt{249}y\right)x}{-11\sqrt{249}y}=\frac{301290-448200y}{-11\sqrt{249}y}$$

Dividing by -11\sqrt{249}y undoes the multiplication by -11\sqrt{249}y.

$$x=\frac{301290-448200y}{-11\sqrt{249}y}$$

Divide 301290-448200y by -11\sqrt{249}y.

$$x=-\frac{10\sqrt{249}\left(121-180y\right)}{11y}$$

Solve for y

$$y=\frac{301290}{-11\sqrt{249}x+448200}$$

$$x\neq \frac{1800\sqrt{249}}{11}$$

Steps for Solving Linear Equation

Subtract 0.1 from 1 to get 0.9.

$$0.1=2y\left(\frac{0.9}{1+0.1}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Add 1 and 0.1 to get 1.1.

$$0.1=2y\left(\frac{0.9}{1.1}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Expand \frac{0.9}{1.1} by multiplying both numerator and the denominator by 10.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{\sqrt{9960000}}\right)-1$$

Factor 9960000=200^{2}\times 249. Rewrite the square root of the product \sqrt{200^{2}\times 249} as the product of square roots \sqrt{200^{2}}\sqrt{249}. Take the square root of 200^{2}.

$$0.1=2y\left(\frac{9}{11}-\frac{x}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{x}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.1=2y\left(\frac{9}{11}-\frac{x\sqrt{249}}{49800}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11 and 49800 is 547800. Multiply \frac{9}{11} times \frac{49800}{49800}. Multiply \frac{x\sqrt{249}}{49800} times \frac{11}{11}.

$$0.1=2y\left(\frac{9\times 49800}{547800}-\frac{11x\sqrt{249}}{547800}\right)-1$$

Since \frac{9\times 49800}{547800} and \frac{11x\sqrt{249}}{547800} have the same denominator, subtract them by subtracting their numerators.

$$0.1=2y\times \frac{9\times 49800-11x\sqrt{249}}{547800}-1$$

Do the multiplications in 9\times 49800-11x\sqrt{249}.

$$0.1=2y\times \frac{448200-11x\sqrt{249}}{547800}-1$$

Cancel out 547800, the greatest common factor in 2 and 547800.

$$0.1=\frac{448200-11x\sqrt{249}}{273900}y-1$$

Express \frac{448200-11x\sqrt{249}}{273900}y as a single fraction.

$$0.1=\frac{\left(448200-11x\sqrt{249}\right)y}{273900}-1$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\left(448200-11x\sqrt{249}\right)y}{273900}-1=0.1$$

Use the distributive property to multiply 448200-11x\sqrt{249} by y.

$$\frac{448200y-11x\sqrt{249}y}{273900}-1=0.1$$

Add 1 to both sides.

$$\frac{448200y-11x\sqrt{249}y}{273900}=0.1+1$$

Add 0.1 and 1 to get 1.1.

$$\frac{448200y-11x\sqrt{249}y}{273900}=1.1$$

Multiply both sides by 273900.

$$448200y-11x\sqrt{249}y=1.1\times 273900$$

Multiply 1.1 and 273900 to get 301290.

$$448200y-11x\sqrt{249}y=301290$$

Combine all terms containing y.

$$\left(448200-11x\sqrt{249}\right)y=301290$$

The equation is in standard form.

$$\left(-11\sqrt{249}x+448200\right)y=301290$$

Divide both sides by 448200-11x\sqrt{249}.

$$\frac{\left(-11\sqrt{249}x+448200\right)y}{-11\sqrt{249}x+448200}=\frac{301290}{-11\sqrt{249}x+448200}$$

Dividing by 448200-11x\sqrt{249} undoes the multiplication by 448200-11x\sqrt{249}.

$$y=\frac{301290}{-11\sqrt{249}x+448200}$$