Solve 0.03=2xleft(1-100/sqrt{9.96*10^6}right)-1

$$0.03 = 2x \left( 1- \frac{ 100 }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } \right) -1$$

Solve for x

$$x=\frac{103\left(\sqrt{249}+498\right)}{99500}\approx 0.531852388$$

Steps for Solving Linear Equation

Calculate 10 to the power of 6 and get 1000000.

$$0.03=2x\left(1-\frac{100}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.03=2x\left(1-\frac{100}{\sqrt{9960000}}\right)-1$$

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}.

$$0.03=2x\left(1-\frac{100}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{100}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.03=2x\left(1-\frac{100\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.03=2x\left(1-\frac{100\sqrt{249}}{200\times 249}\right)-1$$

Cancel out 100 in both numerator and denominator.

$$0.03=2x\left(1-\frac{\sqrt{249}}{2\times 249}\right)-1$$

Multiply 2 and 249 to get 498.

$$0.03=2x\left(1-\frac{\sqrt{249}}{498}\right)-1$$

Use the distributive property to multiply 2x by 1-\frac{\sqrt{249}}{498}.

$$0.03=2x+2x\left(-\frac{\sqrt{249}}{498}\right)-1$$

Cancel out 498, the greatest common factor in 2 and 498.

$$0.03=2x+\frac{\sqrt{249}}{-249}x-1$$

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

$$0.03=2x+\frac{\sqrt{249}x}{-249}-1$$

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

$$2x+\frac{\sqrt{249}x}{-249}-1=0.03$$

Add 1 to both sides.

$$2x+\frac{\sqrt{249}x}{-249}=0.03+1$$

Add 0.03 and 1 to get 1.03.

$$2x+\frac{\sqrt{249}x}{-249}=1.03$$

Multiply both sides of the equation by -249.

$$-498x+\sqrt{249}x=-256.47$$

Combine all terms containing x.

$$\left(-498+\sqrt{249}\right)x=-256.47$$

The equation is in standard form.

$$\left(\sqrt{249}-498\right)x=-256.47$$

Divide both sides by -498+\sqrt{249}.

$$\frac{\left(\sqrt{249}-498\right)x}{\sqrt{249}-498}=-\frac{256.47}{\sqrt{249}-498}$$

Dividing by -498+\sqrt{249} undoes the multiplication by -498+\sqrt{249}.

$$x=-\frac{256.47}{\sqrt{249}-498}$$

Divide -256.47 by -498+\sqrt{249}.

$$x=\frac{103\sqrt{249}}{99500}+\frac{25647}{49750}$$