Solve x^2-x211*10000/6*50000+5948.4375*10000^2/36*50000^2=0

$${ x }^{ 2 } - \frac{ x211 \cdot 10000 }{ 6 \cdot 50000 } + \frac{ 5948.4375 \times { 10000 }^{ 2 } }{ 36 \times { 50000 }^{ 2 } } = 0$$

Solve for x_211

$$x_{211}=30x^{2}+198.28125$$

Steps for Solving Linear Equation

Cancel out 2\times 5000 in both numerator and denominator.

$$x^{2}-\frac{x_{211}}{3\times 10}+\frac{5948.4375\times 10000^{2}}{36\times 50000^{2}}=0$$

Multiply 3 and 10 to get 30.

$$x^{2}-\frac{x_{211}}{30}+\frac{5948.4375\times 10000^{2}}{36\times 50000^{2}}=0$$

Calculate 10000 to the power of 2 and get 100000000.

$$x^{2}-\frac{x_{211}}{30}+\frac{5948.4375\times 100000000}{36\times 50000^{2}}=0$$

Multiply 5948.4375 and 100000000 to get 594843750000.

$$x^{2}-\frac{x_{211}}{30}+\frac{594843750000}{36\times 50000^{2}}=0$$

Calculate 50000 to the power of 2 and get 2500000000.

$$x^{2}-\frac{x_{211}}{30}+\frac{594843750000}{36\times 2500000000}=0$$

Multiply 36 and 2500000000 to get 90000000000.

$$x^{2}-\frac{x_{211}}{30}+\frac{594843750000}{90000000000}=0$$

Reduce the fraction \frac{594843750000}{90000000000} to lowest terms by extracting and canceling out 1406250000.

$$x^{2}-\frac{x_{211}}{30}+\frac{423}{64}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30 and 64 is 960. Multiply \frac{x_{211}}{30} times \frac{32}{32}. Multiply \frac{423}{64} times \frac{15}{15}.

$$x^{2}-\frac{32x_{211}}{960}+\frac{423\times 15}{960}=0$$

Since -\frac{32x_{211}}{960} and \frac{423\times 15}{960} have the same denominator, add them by adding their numerators.

$$x^{2}+\frac{-32x_{211}+423\times 15}{960}=0$$

Do the multiplications in -32x_{211}+423\times 15.

$$x^{2}+\frac{-32x_{211}+6345}{960}=0$$

Divide each term of -32x_{211}+6345 by 960 to get -\frac{1}{30}x_{211}+\frac{423}{64}.

$$x^{2}-\frac{1}{30}x_{211}+\frac{423}{64}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{30}x_{211}+\frac{423}{64}=-x^{2}$$

Subtract \frac{423}{64} from both sides.

$$-\frac{1}{30}x_{211}=-x^{2}-\frac{423}{64}$$

Multiply both sides by -30.

$$\frac{-\frac{1}{30}x_{211}}{-\frac{1}{30}}=\frac{-x^{2}-\frac{423}{64}}{-\frac{1}{30}}$$

Dividing by -\frac{1}{30} undoes the multiplication by -\frac{1}{30}.

$$x_{211}=\frac{-x^{2}-\frac{423}{64}}{-\frac{1}{30}}$$

Divide -x^{2}-\frac{423}{64} by -\frac{1}{30} by multiplying -x^{2}-\frac{423}{64} by the reciprocal of -\frac{1}{30}.

$$x_{211}=30x^{2}+\frac{6345}{32}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{480x_{211}-95175}}{120}$$

$$x=\frac{\sqrt{480x_{211}-95175}}{120}$$

Solve for x

$$x=\frac{\sqrt{480x_{211}-95175}}{120}$$

$$x=-\frac{\sqrt{480x_{211}-95175}}{120}\text{, }x_{211}\geq \frac{6345}{32}$$