Solve 1000=1.1y/2sqrt{9.96*10^6}(1-1/sqrt{1+frac{0.05{pix^2}}})

$$1000=1.1 \frac{ y }{ 2 } \sqrt{ 9.96 \times { 10 }^{ 6 } } (1- \frac{ 1 }{ \sqrt{ 1+ \frac{ 0.05 }{ \pi { x }^{ 2 } } } } )$$

Solve for y (complex solution)

$$y=\frac{100\sqrt{249}\left(20\sqrt{\frac{\pi \left(\pi x^{2}+0.05\right)}{x^{2}}}x^{2}+20\pi x^{2}+1\right)}{2739}$$

$$x\neq 0\text{ and }x\neq \frac{-i}{2\sqrt{5\pi }}\text{ and }x\neq \frac{i}{2\sqrt{5\pi }}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2000=1.1y\sqrt{9.96\times 10^{6}}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$2000=1.1y\sqrt{9.96\times 1000000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Multiply 9.96 and 1000000 to get 9960000.

$$2000=1.1y\sqrt{9960000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

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}.

$$2000=1.1y\times 200\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Multiply 1.1 and 200 to get 220.

$$2000=220y\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Use the distributive property to multiply 220y\sqrt{249} by 1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}.

$$2000=220y\sqrt{249}+220y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

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

$$220y\sqrt{249}+220y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)=2000$$

Multiply 220 and -1 to get -220.

$$220y\sqrt{249}-220y\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}=2000$$

Combine all terms containing y.

$$\left(220\sqrt{249}-220\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)y=2000$$

The equation is in standard form.

$$\left(-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}\right)y=2000$$

Divide both sides by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$\frac{\left(-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}\right)y}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}=\frac{2000}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}$$

Dividing by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1} undoes the multiplication by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$y=\frac{2000}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}$$

Divide 2000 by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$y=\frac{100\sqrt{249\pi +\frac{249}{20x^{2}}}}{249\left(11\sqrt{\pi +\frac{1}{20x^{2}}}-11\sqrt{\pi }\right)}$$

Solve for y

$$y=-\frac{100\sqrt{249\pi x^{2}+12.45}}{2739\left(-\sqrt{\pi x^{2}+0.05}+\sqrt{\pi }|x|\right)}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2000=1.1y\sqrt{9.96\times 10^{6}}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$2000=1.1y\sqrt{9.96\times 1000000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Multiply 9.96 and 1000000 to get 9960000.

$$2000=1.1y\sqrt{9960000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

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}.

$$2000=1.1y\times 200\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Multiply 1.1 and 200 to get 220.

$$2000=220y\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

Use the distributive property to multiply 220y\sqrt{249} by 1-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}.

$$2000=220y\sqrt{249}+220y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)$$

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

$$220y\sqrt{249}+220y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)=2000$$

Multiply 220 and -1 to get -220.

$$220y\sqrt{249}-220y\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}=2000$$

Combine all terms containing y.

$$\left(220\sqrt{249}-220\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi x^{2}}}}\right)y=2000$$

The equation is in standard form.

$$\left(-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}\right)y=2000$$

Divide both sides by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$\frac{\left(-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}\right)y}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}=\frac{2000}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}$$

Dividing by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1} undoes the multiplication by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$y=\frac{2000}{-\frac{220\sqrt{249}}{\sqrt{1+\frac{1}{20\pi x^{2}}}}+220\sqrt{249}}$$

Divide 2000 by 220\sqrt{249}-220\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}x^{-2}}\right)^{-1}.

$$y=-\frac{100\sqrt{249\pi x^{2}+12.45}}{2739\left(-\sqrt{\pi x^{2}+0.05}+\sqrt{\pi }|x|\right)}$$

Solve for x (complex solution)

$$x=-\frac{i\left(\pi \left(11\sqrt{249}y-50\right)\right)^{-0.5}\sqrt{10\left(-30129y^{2}+2200\sqrt{249}y-10000\right)}}{200}$$

$$x=\frac{i\left(\pi \left(11\sqrt{249}y-50\right)\right)^{-0.5}\sqrt{10\left(-30129y^{2}+2200\sqrt{249}y-10000\right)}}{200}\text{, }y\neq \frac{50\sqrt{249}}{2739}\text{ and }y\neq 0\text{ and }y\neq \frac{100\sqrt{249}}{2739}\text{ and }|arg(\sqrt{\frac{y^{2}}{\left(-2739y+100\sqrt{249}\right)^{2}}}\left(-2739y+100\sqrt{249}\right))-arg(-y)|<\pi$$

Solve for x

$$x=\frac{\sqrt{\frac{2490\left(11\sqrt{249}y+50\right)}{\pi \left(30129y^{2}-2500\right)}}\left(-2739y+100\sqrt{249}\right)}{49800}$$

$$x=-\frac{\sqrt{\frac{2490\left(11\sqrt{249}y+50\right)}{\pi \left(30129y^{2}-2500\right)}}\left(-2739y+100\sqrt{249}\right)}{49800}\text{, }y>\frac{100\sqrt{249}}{2739}$$