Solve 0.4=2*x(1-263/sqrt{9.96*10^6})-1

$$0.4=2 \times x(1- \frac{ 263 }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x=\frac{36820\sqrt{249}+6972000}{9890831}\approx 0.763637535$$

Steps for Solving Linear Equation

Calculate 10 to the power of 6 and get 1000000.

$$0.4=2x\left(1-\frac{263}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.4=2x\left(1-\frac{263}{\sqrt{9960000}}\right)-1$$

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}.

$$0.4=2x\left(1-\frac{263}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{263}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.4=2x\left(1-\frac{263\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.4=2x\left(1-\frac{263\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.4=2x\left(1-\frac{263\sqrt{249}}{49800}\right)-1$$

Use the distributive property to multiply 2x by 1-\frac{263\sqrt{249}}{49800}.

$$0.4=2x+2x\left(-\frac{263\sqrt{249}}{49800}\right)-1$$

Cancel out 49800, the greatest common factor in 2 and 49800.

$$0.4=2x+\frac{263\sqrt{249}}{-24900}x-1$$

Express \frac{263\sqrt{249}}{-24900}x as a single fraction.

$$0.4=2x+\frac{263\sqrt{249}x}{-24900}-1$$

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

$$2x+\frac{263\sqrt{249}x}{-24900}-1=0.4$$

Add 1 to both sides.

$$2x+\frac{263\sqrt{249}x}{-24900}=0.4+1$$

Add 0.4 and 1 to get 1.4.

$$2x+\frac{263\sqrt{249}x}{-24900}=1.4$$

Multiply both sides of the equation by -24900.

$$-49800x+263\sqrt{249}x=-34860$$

Combine all terms containing x.

$$\left(-49800+263\sqrt{249}\right)x=-34860$$

The equation is in standard form.

$$\left(263\sqrt{249}-49800\right)x=-34860$$

Divide both sides by -49800+263\sqrt{249}.

$$\frac{\left(263\sqrt{249}-49800\right)x}{263\sqrt{249}-49800}=-\frac{34860}{263\sqrt{249}-49800}$$

Dividing by -49800+263\sqrt{249} undoes the multiplication by -49800+263\sqrt{249}.

$$x=-\frac{34860}{263\sqrt{249}-49800}$$

Divide -34860 by -49800+263\sqrt{249}.

$$x=\frac{36820\sqrt{249}+6972000}{9890831}$$