Solve 522^2x+52^2+xdiv9=64x+sqrt{5}*53x-536^2

$${ 522 }^{ 2 } x+ { 52 }^{ 2 } +x \div 9 = 64x+ \sqrt{ 5 } \times 53x- { 536 }^{ 2 }$$

Solve for x

$$x=\frac{-311242500\sqrt{5}-1599787102500}{1502807233579}\approx -1.06499558$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9.

$$9\times 522^{2}x+9\times 52^{2}+x=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Calculate 522 to the power of 2 and get 272484.

$$9\times 272484x+9\times 52^{2}+x=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Multiply 9 and 272484 to get 2452356.

$$2452356x+9\times 52^{2}+x=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Calculate 52 to the power of 2 and get 2704.

$$2452356x+9\times 2704+x=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Multiply 9 and 2704 to get 24336.

$$2452356x+24336+x=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Combine 2452356x and x to get 2452357x.

$$2452357x+24336=9\left(64x+53\sqrt{5}x\right)-9\times 536^{2}$$

Use the distributive property to multiply 9 by 64x+53\sqrt{5}x.

$$2452357x+24336=576x+477\sqrt{5}x-9\times 536^{2}$$

Calculate 536 to the power of 2 and get 287296.

$$2452357x+24336=576x+477\sqrt{5}x-9\times 287296$$

Multiply 9 and 287296 to get 2585664.

$$2452357x+24336=576x+477\sqrt{5}x-2585664$$

Subtract 576x from both sides.

$$2452357x+24336-576x=477\sqrt{5}x-2585664$$

Combine 2452357x and -576x to get 2451781x.

$$2451781x+24336=477\sqrt{5}x-2585664$$

Subtract 477\sqrt{5}x from both sides.

$$2451781x+24336-477\sqrt{5}x=-2585664$$

Subtract 24336 from both sides.

$$2451781x-477\sqrt{5}x=-2585664-24336$$

Subtract 24336 from -2585664 to get -2610000.

$$2451781x-477\sqrt{5}x=-2610000$$

Combine all terms containing x.

$$\left(2451781-477\sqrt{5}\right)x=-2610000$$

Divide both sides by 2451781-477\sqrt{5}.

$$\frac{\left(2451781-477\sqrt{5}\right)x}{2451781-477\sqrt{5}}=-\frac{2610000}{2451781-477\sqrt{5}}$$

Dividing by 2451781-477\sqrt{5} undoes the multiplication by 2451781-477\sqrt{5}.

$$x=-\frac{2610000}{2451781-477\sqrt{5}}$$

Divide -2610000 by 2451781-477\sqrt{5}.

$$x=\frac{-311242500\sqrt{5}-1599787102500}{1502807233579}$$