Solve (1.21-x)*10000+10000=12263.6304/x

$$(1.21-x) \times 10000+10000= \frac{ 12263.6304 }{ x }$$

Solve for x (complex solution)

$$x=\frac{i\sqrt{133451}}{5000}+1.105\approx 1.105+0.073061892i$$

$$x=-\frac{i\sqrt{133451}}{5000}+1.105\approx 1.105-0.073061892i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\left(1.21-x\right)\times 10000x+x\times 10000=12263.6304$$

Use the distributive property to multiply 1.21-x by 10000.

$$\left(12100-10000x\right)x+x\times 10000=12263.6304$$

Use the distributive property to multiply 12100-10000x by x.

$$12100x-10000x^{2}+x\times 10000=12263.6304$$

Combine 12100x and x\times 10000 to get 22100x.

$$22100x-10000x^{2}=12263.6304$$

Subtract 12263.6304 from both sides.

$$22100x-10000x^{2}-12263.6304=0$$

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.

$$-10000x^{2}+22100x-12263.6304=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10000 for a, 22100 for b, and -12263.6304 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-22100±\sqrt{22100^{2}-4\left(-10000\right)\left(-12263.6304\right)}}{2\left(-10000\right)}$$

Square 22100.

$$x=\frac{-22100±\sqrt{488410000-4\left(-10000\right)\left(-12263.6304\right)}}{2\left(-10000\right)}$$

Multiply -4 times -10000.

$$x=\frac{-22100±\sqrt{488410000+40000\left(-12263.6304\right)}}{2\left(-10000\right)}$$

Multiply 40000 times -12263.6304.

$$x=\frac{-22100±\sqrt{488410000-490545216}}{2\left(-10000\right)}$$

Add 488410000 to -490545216.

$$x=\frac{-22100±\sqrt{-2135216}}{2\left(-10000\right)}$$

Take the square root of -2135216.

$$x=\frac{-22100±4\sqrt{133451}i}{2\left(-10000\right)}$$

Multiply 2 times -10000.

$$x=\frac{-22100±4\sqrt{133451}i}{-20000}$$

Now solve the equation x=\frac{-22100±4\sqrt{133451}i}{-20000} when ± is plus. Add -22100 to 4i\sqrt{133451}.

$$x=\frac{-22100+4\sqrt{133451}i}{-20000}$$

Divide -22100+4i\sqrt{133451} by -20000.

$$x=-\frac{\sqrt{133451}i}{5000}+\frac{221}{200}$$

Now solve the equation x=\frac{-22100±4\sqrt{133451}i}{-20000} when ± is minus. Subtract 4i\sqrt{133451} from -22100.

$$x=\frac{-4\sqrt{133451}i-22100}{-20000}$$

Divide -22100-4i\sqrt{133451} by -20000.

$$x=\frac{\sqrt{133451}i}{5000}+\frac{221}{200}$$

The equation is now solved.

$$x=-\frac{\sqrt{133451}i}{5000}+\frac{221}{200} x=\frac{\sqrt{133451}i}{5000}+\frac{221}{200}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\left(1.21-x\right)\times 10000x+x\times 10000=12263.6304$$

Use the distributive property to multiply 1.21-x by 10000.

$$\left(12100-10000x\right)x+x\times 10000=12263.6304$$

Use the distributive property to multiply 12100-10000x by x.

$$12100x-10000x^{2}+x\times 10000=12263.6304$$

Combine 12100x and x\times 10000 to get 22100x.

$$22100x-10000x^{2}=12263.6304$$

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.

$$-10000x^{2}+22100x=12263.6304$$

Divide both sides by -10000.

$$\frac{-10000x^{2}+22100x}{-10000}=\frac{12263.6304}{-10000}$$

Dividing by -10000 undoes the multiplication by -10000.

$$x^{2}+\frac{22100}{-10000}x=\frac{12263.6304}{-10000}$$

Reduce the fraction \frac{22100}{-10000} to lowest terms by extracting and canceling out 100.

$$x^{2}-\frac{221}{100}x=\frac{12263.6304}{-10000}$$

Divide 12263.6304 by -10000.

$$x^{2}-\frac{221}{100}x=-1.22636304$$

Divide -\frac{221}{100}, the coefficient of the x term, by 2 to get -\frac{221}{200}. Then add the square of -\frac{221}{200} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{221}{100}x+\left(-\frac{221}{200}\right)^{2}=-1.22636304+\left(-\frac{221}{200}\right)^{2}$$

Square -\frac{221}{200} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{221}{100}x+\frac{48841}{40000}=-1.22636304+\frac{48841}{40000}$$

Add -1.22636304 to \frac{48841}{40000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{221}{100}x+\frac{48841}{40000}=-\frac{133451}{25000000}$$

Factor x^{2}-\frac{221}{100}x+\frac{48841}{40000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{221}{200}\right)^{2}=-\frac{133451}{25000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{221}{200}\right)^{2}}=\sqrt{-\frac{133451}{25000000}}$$

Simplify.

$$x-\frac{221}{200}=\frac{\sqrt{133451}i}{5000} x-\frac{221}{200}=-\frac{\sqrt{133451}i}{5000}$$

Add \frac{221}{200} to both sides of the equation.

$$x=\frac{\sqrt{133451}i}{5000}+\frac{221}{200} x=-\frac{\sqrt{133451}i}{5000}+\frac{221}{200}$$