Solve 1000=left(1+0.05right)frac{xsqrt{9.9610^6}}{2}left(1-1/sqrt{1+frac{0.05{pi}}}right)

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

Solve for x

$$x = \frac{4000 \sqrt{249 \pi + 12.45} {(\sqrt{\pi + 0.05} + \sqrt{\pi})}}{5229} \approx 76.748070047$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

Add 1 and 0.05 to get 1.05.

$$2000=1.05x\sqrt{9.96\times 10^{6}}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$2000=1.05x\sqrt{9.96\times 1000000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

Multiply 9.96 and 1000000 to get 9960000.

$$2000=1.05x\sqrt{9960000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

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}.

$$2000=1.05x\times 200\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

Multiply 1.05 and 200 to get 210.

$$2000=210x\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

Use the distributive property to multiply 210x\sqrt{249} by 1-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}.

$$2000=210x\sqrt{249}+210x\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)$$

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

$$210x\sqrt{249}+210x\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)=2000$$

Multiply 210 and -1 to get -210.

$$210x\sqrt{249}-210x\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi }}}=2000$$

Combine all terms containing x.

$$\left(210\sqrt{249}-210\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi }}}\right)x=2000$$

The equation is in standard form.

$$\left(-\frac{210\sqrt{249}}{\sqrt{\frac{1}{20\pi }+1}}+210\sqrt{249}\right)x=2000$$

Divide both sides by 210\sqrt{249}-210\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}}\right)^{-1}.

$$\frac{\left(-\frac{210\sqrt{249}}{\sqrt{\frac{1}{20\pi }+1}}+210\sqrt{249}\right)x}{-\frac{210\sqrt{249}}{\sqrt{\frac{1}{20\pi }+1}}+210\sqrt{249}}=\frac{2000}{-\frac{210\sqrt{249}}{\sqrt{\frac{1}{20\pi }+1}}+210\sqrt{249}}$$

Dividing by 210\sqrt{249}-210\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}}\right)^{-1} undoes the multiplication by 210\sqrt{249}-210\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}}\right)^{-1}.

$$x=\frac{2000}{-\frac{210\sqrt{249}}{\sqrt{\frac{1}{20\pi }+1}}+210\sqrt{249}}$$

Divide 2000 by 210\sqrt{249}-210\sqrt{249}\left(\sqrt{1+0.05\pi ^{-1}}\right)^{-1}.

$$x=\frac{4000\sqrt{249\pi +12.45}\left(\sqrt{\pi +0.05}+\sqrt{\pi }\right)}{5229}$$