Solve y=4x(1-2500/sqrt{9.96*10^6})-1

$$y=4x(1- \frac{ 2500 }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x=\frac{\left(25\sqrt{249}+498\right)\left(y+1\right)}{742}$$

Steps for Solving Linear Equation

Calculate 10 to the power of 6 and get 1000000.

$$y=4x\left(1-\frac{2500}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$y=4x\left(1-\frac{2500}{\sqrt{9960000}}\right)-1$$

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}.

$$y=4x\left(1-\frac{2500}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{2500}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$y=4x\left(1-\frac{2500\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$y=4x\left(1-\frac{2500\sqrt{249}}{200\times 249}\right)-1$$

Cancel out 100 in both numerator and denominator.

$$y=4x\left(1-\frac{25\sqrt{249}}{2\times 249}\right)-1$$

Multiply 2 and 249 to get 498.

$$y=4x\left(1-\frac{25\sqrt{249}}{498}\right)-1$$

Use the distributive property to multiply 4x by 1-\frac{25\sqrt{249}}{498}.

$$y=4x+4x\left(-\frac{25\sqrt{249}}{498}\right)-1$$

Express 4\left(-\frac{25\sqrt{249}}{498}\right) as a single fraction.

$$y=4x+\frac{-4\times 25\sqrt{249}}{498}x-1$$

Multiply -4 and 25 to get -100.

$$y=4x+\frac{-100\sqrt{249}}{498}x-1$$

Divide -100\sqrt{249} by 498 to get -\frac{50}{249}\sqrt{249}.

$$y=4x-\frac{50}{249}\sqrt{249}x-1$$

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

$$4x-\frac{50}{249}\sqrt{249}x-1=y$$

Add 1 to both sides.

$$4x-\frac{50}{249}\sqrt{249}x=y+1$$

Combine all terms containing x.

$$\left(4-\frac{50}{249}\sqrt{249}\right)x=y+1$$

The equation is in standard form.

$$\left(-\frac{50\sqrt{249}}{249}+4\right)x=y+1$$

Divide both sides by 4-\frac{50}{249}\sqrt{249}.

$$\frac{\left(-\frac{50\sqrt{249}}{249}+4\right)x}{-\frac{50\sqrt{249}}{249}+4}=\frac{y+1}{-\frac{50\sqrt{249}}{249}+4}$$

Dividing by 4-\frac{50}{249}\sqrt{249} undoes the multiplication by 4-\frac{50}{249}\sqrt{249}.

$$x=\frac{y+1}{-\frac{50\sqrt{249}}{249}+4}$$

Divide y+1 by 4-\frac{50}{249}\sqrt{249}.

$$x=\frac{\left(25\sqrt{249}+498\right)\left(y+1\right)}{742}$$

Solve for y

$$y=-\frac{50\sqrt{249}x}{249}+4x-1$$