Solve 500*(40%+2x%)*2*(1-3/10x%)+250*(20%+6x%)*2*(1-1/4x%)=2500x%

$$500 \times (40 \% +2x \% ) \times 2 \times (1- \frac{ 3 }{ 10 } x \% )+250 \times (20 \% +6x \% ) \times 2 \times (1- \frac{ 1 }{ 4 } x \% )=2500x \%$$

Solve for x

$$x = \frac{5 \sqrt{36649} + 785}{9} \approx 193.577380786$$

$$x=\frac{785-5\sqrt{36649}}{9}\approx -19.132936341$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 100, the least common multiple of 100,10,4.

$$50000\left(\frac{40}{100}+2\times \frac{x}{100}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$50000\left(\frac{2}{5}+2\times \frac{x}{100}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 100, the greatest common factor in 2 and 100.

$$50000\left(\frac{2}{5}+\frac{x}{50}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 50 is 50. Multiply \frac{2}{5} times \frac{10}{10}.

$$50000\left(\frac{2\times 10}{50}+\frac{x}{50}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Since \frac{2\times 10}{50} and \frac{x}{50} have the same denominator, add them by adding their numerators.

$$50000\times \frac{2\times 10+x}{50}\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Do the multiplications in 2\times 10+x.

$$50000\times \frac{20+x}{50}\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 50000 and 2 to get 100000.

$$100000\times \frac{20+x}{50}\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply \frac{3}{10} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$100000\times \frac{20+x}{50}\left(1-\frac{3x}{10\times 100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 10 and 100 to get 1000.

$$100000\times \frac{20+x}{50}\left(1-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 50, the greatest common factor in 100000 and 50.

$$2000\left(20+x\right)\left(1-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply 2000\left(20+x\right) by 1-\frac{3x}{1000}.

$$2000\left(20+x\right)+2000\left(20+x\right)\left(-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply 2000 by 20+x.

$$40000+2000x+2000\left(20+x\right)\left(-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 1000, the greatest common factor in 2000 and 1000.

$$40000+2000x-2\times 3x\left(20+x\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply -2\times 3x by 20+x.

$$40000+2000x-120x-6x^{2}+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Combine 2000x and -120x to get 1880x.

$$40000+1880x-6x^{2}+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$40000+1880x-6x^{2}+25000\left(\frac{1}{5}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Express 6\times \frac{x}{100} as a single fraction.

$$40000+1880x-6x^{2}+25000\left(\frac{1}{5}+\frac{6x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 100 is 100. Multiply \frac{1}{5} times \frac{20}{20}.

$$40000+1880x-6x^{2}+25000\left(\frac{20}{100}+\frac{6x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Since \frac{20}{100} and \frac{6x}{100} have the same denominator, add them by adding their numerators.

$$40000+1880x-6x^{2}+25000\times \frac{20+6x}{100}\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 25000 and 2 to get 50000.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply \frac{1}{4} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{x}{4\times 100}\right)=2500x$$

Multiply 4 and 100 to get 400.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{x}{400}\right)=2500x$$

Cancel out 100, the greatest common factor in 50000 and 100.

$$40000+1880x-6x^{2}+500\left(20+6x\right)\left(1-\frac{x}{400}\right)=2500x$$

Use the distributive property to multiply 500\left(20+6x\right) by 1-\frac{x}{400}.

$$40000+1880x-6x^{2}+500\left(20+6x\right)+500\left(20+6x\right)\left(-\frac{x}{400}\right)=2500x$$

Use the distributive property to multiply 500 by 20+6x.

$$40000+1880x-6x^{2}+10000+3000x+500\left(20+6x\right)\left(-\frac{x}{400}\right)=2500x$$

Express 500\left(-\frac{x}{400}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x+\frac{-500x}{400}\left(20+6x\right)=2500x$$

Use the distributive property to multiply \frac{-500x}{400} by 20+6x.

$$40000+1880x-6x^{2}+10000+3000x+20\times \frac{-500x}{400}+6\times \frac{-500x}{400}x=2500x$$

Divide -500x by 400 to get -\frac{5}{4}x.

$$40000+1880x-6x^{2}+10000+3000x+20\left(-\frac{5}{4}\right)x+6\times \frac{-500x}{400}x=2500x$$

Express 20\left(-\frac{5}{4}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x+\frac{20\left(-5\right)}{4}x+6\times \frac{-500x}{400}x=2500x$$

Multiply 20 and -5 to get -100.

$$40000+1880x-6x^{2}+10000+3000x+\frac{-100}{4}x+6\times \frac{-500x}{400}x=2500x$$

Divide -100 by 4 to get -25.

$$40000+1880x-6x^{2}+10000+3000x-25x+6\times \frac{-500x}{400}x=2500x$$

Divide -500x by 400 to get -\frac{5}{4}x.

$$40000+1880x-6x^{2}+10000+3000x-25x+6\left(-\frac{5}{4}\right)xx=2500x$$

Express 6\left(-\frac{5}{4}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x-25x+\frac{6\left(-5\right)}{4}xx=2500x$$

Multiply 6 and -5 to get -30.

$$40000+1880x-6x^{2}+10000+3000x-25x+\frac{-30}{4}xx=2500x$$

Reduce the fraction \frac{-30}{4} to lowest terms by extracting and canceling out 2.

$$40000+1880x-6x^{2}+10000+3000x-25x-\frac{15}{2}xx=2500x$$

Multiply x and x to get x^{2}.

$$40000+1880x-6x^{2}+10000+3000x-25x-\frac{15}{2}x^{2}=2500x$$

Combine 3000x and -25x to get 2975x.

$$40000+1880x-6x^{2}+10000+2975x-\frac{15}{2}x^{2}=2500x$$

Add 40000 and 10000 to get 50000.

$$50000+1880x-6x^{2}+2975x-\frac{15}{2}x^{2}=2500x$$

Combine 1880x and 2975x to get 4855x.

$$50000+4855x-6x^{2}-\frac{15}{2}x^{2}=2500x$$

Combine -6x^{2} and -\frac{15}{2}x^{2} to get -\frac{27}{2}x^{2}.

$$50000+4855x-\frac{27}{2}x^{2}=2500x$$

Subtract 2500x from both sides.

$$50000+4855x-\frac{27}{2}x^{2}-2500x=0$$

Combine 4855x and -2500x to get 2355x.

$$50000+2355x-\frac{27}{2}x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-\frac{27}{2}x^{2}+2355x+50000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{27}{2} for a, 2355 for b, and 50000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2355±\sqrt{2355^{2}-4\left(-\frac{27}{2}\right)\times 50000}}{2\left(-\frac{27}{2}\right)}$$

Square 2355.

$$x=\frac{-2355±\sqrt{5546025-4\left(-\frac{27}{2}\right)\times 50000}}{2\left(-\frac{27}{2}\right)}$$

Multiply -4 times -\frac{27}{2}.

$$x=\frac{-2355±\sqrt{5546025+54\times 50000}}{2\left(-\frac{27}{2}\right)}$$

Multiply 54 times 50000.

$$x=\frac{-2355±\sqrt{5546025+2700000}}{2\left(-\frac{27}{2}\right)}$$

Add 5546025 to 2700000.

$$x=\frac{-2355±\sqrt{8246025}}{2\left(-\frac{27}{2}\right)}$$

Take the square root of 8246025.

$$x=\frac{-2355±15\sqrt{36649}}{2\left(-\frac{27}{2}\right)}$$

Multiply 2 times -\frac{27}{2}.

$$x=\frac{-2355±15\sqrt{36649}}{-27}$$

Now solve the equation x=\frac{-2355±15\sqrt{36649}}{-27} when ± is plus. Add -2355 to 15\sqrt{36649}.

$$x=\frac{15\sqrt{36649}-2355}{-27}$$

Divide -2355+15\sqrt{36649} by -27.

$$x=\frac{785-5\sqrt{36649}}{9}$$

Now solve the equation x=\frac{-2355±15\sqrt{36649}}{-27} when ± is minus. Subtract 15\sqrt{36649} from -2355.

$$x=\frac{-15\sqrt{36649}-2355}{-27}$$

Divide -2355-15\sqrt{36649} by -27.

$$x=\frac{5\sqrt{36649}+785}{9}$$

The equation is now solved.

$$x=\frac{785-5\sqrt{36649}}{9} x=\frac{5\sqrt{36649}+785}{9}$$

Steps for Completing the Square

Multiply both sides of the equation by 100, the least common multiple of 100,10,4.

$$50000\left(\frac{40}{100}+2\times \frac{x}{100}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$50000\left(\frac{2}{5}+2\times \frac{x}{100}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 100, the greatest common factor in 2 and 100.

$$50000\left(\frac{2}{5}+\frac{x}{50}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 50 is 50. Multiply \frac{2}{5} times \frac{10}{10}.

$$50000\left(\frac{2\times 10}{50}+\frac{x}{50}\right)\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Since \frac{2\times 10}{50} and \frac{x}{50} have the same denominator, add them by adding their numerators.

$$50000\times \frac{2\times 10+x}{50}\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Do the multiplications in 2\times 10+x.

$$50000\times \frac{20+x}{50}\times 2\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 50000 and 2 to get 100000.

$$100000\times \frac{20+x}{50}\left(1-\frac{3}{10}\times \frac{x}{100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply \frac{3}{10} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$100000\times \frac{20+x}{50}\left(1-\frac{3x}{10\times 100}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 10 and 100 to get 1000.

$$100000\times \frac{20+x}{50}\left(1-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 50, the greatest common factor in 100000 and 50.

$$2000\left(20+x\right)\left(1-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply 2000\left(20+x\right) by 1-\frac{3x}{1000}.

$$2000\left(20+x\right)+2000\left(20+x\right)\left(-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply 2000 by 20+x.

$$40000+2000x+2000\left(20+x\right)\left(-\frac{3x}{1000}\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Cancel out 1000, the greatest common factor in 2000 and 1000.

$$40000+2000x-2\times 3x\left(20+x\right)+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Use the distributive property to multiply -2\times 3x by 20+x.

$$40000+2000x-120x-6x^{2}+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Combine 2000x and -120x to get 1880x.

$$40000+1880x-6x^{2}+25000\left(\frac{20}{100}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$40000+1880x-6x^{2}+25000\left(\frac{1}{5}+6\times \frac{x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Express 6\times \frac{x}{100} as a single fraction.

$$40000+1880x-6x^{2}+25000\left(\frac{1}{5}+\frac{6x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 100 is 100. Multiply \frac{1}{5} times \frac{20}{20}.

$$40000+1880x-6x^{2}+25000\left(\frac{20}{100}+\frac{6x}{100}\right)\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Since \frac{20}{100} and \frac{6x}{100} have the same denominator, add them by adding their numerators.

$$40000+1880x-6x^{2}+25000\times \frac{20+6x}{100}\times 2\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply 25000 and 2 to get 50000.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{1}{4}\times \frac{x}{100}\right)=2500x$$

Multiply \frac{1}{4} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{x}{4\times 100}\right)=2500x$$

Multiply 4 and 100 to get 400.

$$40000+1880x-6x^{2}+50000\times \frac{20+6x}{100}\left(1-\frac{x}{400}\right)=2500x$$

Cancel out 100, the greatest common factor in 50000 and 100.

$$40000+1880x-6x^{2}+500\left(20+6x\right)\left(1-\frac{x}{400}\right)=2500x$$

Use the distributive property to multiply 500\left(20+6x\right) by 1-\frac{x}{400}.

$$40000+1880x-6x^{2}+500\left(20+6x\right)+500\left(20+6x\right)\left(-\frac{x}{400}\right)=2500x$$

Use the distributive property to multiply 500 by 20+6x.

$$40000+1880x-6x^{2}+10000+3000x+500\left(20+6x\right)\left(-\frac{x}{400}\right)=2500x$$

Express 500\left(-\frac{x}{400}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x+\frac{-500x}{400}\left(20+6x\right)=2500x$$

Use the distributive property to multiply \frac{-500x}{400} by 20+6x.

$$40000+1880x-6x^{2}+10000+3000x+20\times \frac{-500x}{400}+6\times \frac{-500x}{400}x=2500x$$

Divide -500x by 400 to get -\frac{5}{4}x.

$$40000+1880x-6x^{2}+10000+3000x+20\left(-\frac{5}{4}\right)x+6\times \frac{-500x}{400}x=2500x$$

Express 20\left(-\frac{5}{4}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x+\frac{20\left(-5\right)}{4}x+6\times \frac{-500x}{400}x=2500x$$

Multiply 20 and -5 to get -100.

$$40000+1880x-6x^{2}+10000+3000x+\frac{-100}{4}x+6\times \frac{-500x}{400}x=2500x$$

Divide -100 by 4 to get -25.

$$40000+1880x-6x^{2}+10000+3000x-25x+6\times \frac{-500x}{400}x=2500x$$

Divide -500x by 400 to get -\frac{5}{4}x.

$$40000+1880x-6x^{2}+10000+3000x-25x+6\left(-\frac{5}{4}\right)xx=2500x$$

Express 6\left(-\frac{5}{4}\right) as a single fraction.

$$40000+1880x-6x^{2}+10000+3000x-25x+\frac{6\left(-5\right)}{4}xx=2500x$$

Multiply 6 and -5 to get -30.

$$40000+1880x-6x^{2}+10000+3000x-25x+\frac{-30}{4}xx=2500x$$

Reduce the fraction \frac{-30}{4} to lowest terms by extracting and canceling out 2.

$$40000+1880x-6x^{2}+10000+3000x-25x-\frac{15}{2}xx=2500x$$

Multiply x and x to get x^{2}.

$$40000+1880x-6x^{2}+10000+3000x-25x-\frac{15}{2}x^{2}=2500x$$

Combine 3000x and -25x to get 2975x.

$$40000+1880x-6x^{2}+10000+2975x-\frac{15}{2}x^{2}=2500x$$

Add 40000 and 10000 to get 50000.

$$50000+1880x-6x^{2}+2975x-\frac{15}{2}x^{2}=2500x$$

Combine 1880x and 2975x to get 4855x.

$$50000+4855x-6x^{2}-\frac{15}{2}x^{2}=2500x$$

Combine -6x^{2} and -\frac{15}{2}x^{2} to get -\frac{27}{2}x^{2}.

$$50000+4855x-\frac{27}{2}x^{2}=2500x$$

Subtract 2500x from both sides.

$$50000+4855x-\frac{27}{2}x^{2}-2500x=0$$

Combine 4855x and -2500x to get 2355x.

$$50000+2355x-\frac{27}{2}x^{2}=0$$

Subtract 50000 from both sides. Anything subtracted from zero gives its negation.

$$2355x-\frac{27}{2}x^{2}=-50000$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-\frac{27}{2}x^{2}+2355x=-50000$$

Divide both sides of the equation by -\frac{27}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{27}{2}x^{2}+2355x}{-\frac{27}{2}}=-\frac{50000}{-\frac{27}{2}}$$

Dividing by -\frac{27}{2} undoes the multiplication by -\frac{27}{2}.

$$x^{2}+\frac{2355}{-\frac{27}{2}}x=-\frac{50000}{-\frac{27}{2}}$$

Divide 2355 by -\frac{27}{2} by multiplying 2355 by the reciprocal of -\frac{27}{2}.

$$x^{2}-\frac{1570}{9}x=-\frac{50000}{-\frac{27}{2}}$$

Divide -50000 by -\frac{27}{2} by multiplying -50000 by the reciprocal of -\frac{27}{2}.

$$x^{2}-\frac{1570}{9}x=\frac{100000}{27}$$

Divide -\frac{1570}{9}, the coefficient of the x term, by 2 to get -\frac{785}{9}. Then add the square of -\frac{785}{9} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1570}{9}x+\left(-\frac{785}{9}\right)^{2}=\frac{100000}{27}+\left(-\frac{785}{9}\right)^{2}$$

Square -\frac{785}{9} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1570}{9}x+\frac{616225}{81}=\frac{100000}{27}+\frac{616225}{81}$$

Add \frac{100000}{27} to \frac{616225}{81} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{1570}{9}x+\frac{616225}{81}=\frac{916225}{81}$$

Factor x^{2}-\frac{1570}{9}x+\frac{616225}{81}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{785}{9}\right)^{2}=\frac{916225}{81}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{785}{9}\right)^{2}}=\sqrt{\frac{916225}{81}}$$

Simplify.

$$x-\frac{785}{9}=\frac{5\sqrt{36649}}{9} x-\frac{785}{9}=-\frac{5\sqrt{36649}}{9}$$

Add \frac{785}{9} to both sides of the equation.

$$x=\frac{5\sqrt{36649}+785}{9} x=\frac{785-5\sqrt{36649}}{9}$$