Solve 003=2xleft(1-100/sqrt{996*10^6}right)-1

$$003 = 2x \left( 1- \frac{ 100 }{ \sqrt{ 996 \times { 10 }^{ 6 } } } \right) -1$$

Solve for x

$$x=\frac{10\left(\sqrt{249}+4980\right)}{99599}\approx 0.501589347$$

Steps for Solving Linear Equation

Multiply 0 and 0 to get 0.

$$0\times 3=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

Multiply 0 and 3 to get 0.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 1000000}}\right)-1$$

Multiply 996 and 1000000 to get 996000000.

$$0=2x\left(1-\frac{100}{\sqrt{996000000}}\right)-1$$

Factor 996000000=2000^{2}\times 249. Rewrite the square root of the product \sqrt{2000^{2}\times 249} as the product of square roots \sqrt{2000^{2}}\sqrt{249}. Take the square root of 2000^{2}.

$$0=2x\left(1-\frac{100}{2000\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{100}{2000\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\times 249}\right)-1$$

Cancel out 100 in both numerator and denominator.

$$0=2x\left(1-\frac{\sqrt{249}}{20\times 249}\right)-1$$

Multiply 20 and 249 to get 4980.

$$0=2x\left(1-\frac{\sqrt{249}}{4980}\right)-1$$

Use the distributive property to multiply 2x by 1-\frac{\sqrt{249}}{4980}.

$$0=2x+2x\left(-\frac{\sqrt{249}}{4980}\right)-1$$

Cancel out 4980, the greatest common factor in 2 and 4980.

$$0=2x+\frac{\sqrt{249}}{-2490}x-1$$

Express \frac{\sqrt{249}}{-2490}x as a single fraction.

$$0=2x+\frac{\sqrt{249}x}{-2490}-1$$

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

$$2x+\frac{\sqrt{249}x}{-2490}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$2x+\frac{\sqrt{249}x}{-2490}=1$$

Multiply both sides of the equation by -2490.

$$-4980x+\sqrt{249}x=-2490$$

Combine all terms containing x.

$$\left(-4980+\sqrt{249}\right)x=-2490$$

The equation is in standard form.

$$\left(\sqrt{249}-4980\right)x=-2490$$

Divide both sides by -4980+\sqrt{249}.

$$\frac{\left(\sqrt{249}-4980\right)x}{\sqrt{249}-4980}=-\frac{2490}{\sqrt{249}-4980}$$

Dividing by -4980+\sqrt{249} undoes the multiplication by -4980+\sqrt{249}.

$$x=-\frac{2490}{\sqrt{249}-4980}$$

Divide -2490 by -4980+\sqrt{249}.

$$x=\frac{10\sqrt{249}+49800}{99599}$$