Solve (2x)^2/(1-x)(1-5-x)=1.2*10^-2

$$\frac { ( 2 x ) ^ { 2 } } { ( 1 - x ) ( 1 - 5 - x ) } = 1.2 \times 10 ^ { - 2 }$$

Solve for x (complex solution)

$$x=\frac{9+i\times 35\sqrt{39}}{1994}\approx 0.004513541+0.109616314i$$

$$x=\frac{-i\times 35\sqrt{39}+9}{1994}\approx 0.004513541-0.109616314i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -4,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+4\right).

$$\left(2x\right)^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$4x^{2}=1.2\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Multiply 1.2 and \frac{1}{100} to get \frac{3}{250}.

$$4x^{2}=\frac{3}{250}\left(x-1\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{250} by x-1.

$$4x^{2}=\left(\frac{3}{250}x-\frac{3}{250}\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{250}x-\frac{3}{250} by x+4 and combine like terms.

$$4x^{2}=\frac{3}{250}x^{2}+\frac{9}{250}x-\frac{6}{125}$$

Subtract \frac{3}{250}x^{2} from both sides.

$$4x^{2}-\frac{3}{250}x^{2}=\frac{9}{250}x-\frac{6}{125}$$

Combine 4x^{2} and -\frac{3}{250}x^{2} to get \frac{997}{250}x^{2}.

$$\frac{997}{250}x^{2}=\frac{9}{250}x-\frac{6}{125}$$

Subtract \frac{9}{250}x from both sides.

$$\frac{997}{250}x^{2}-\frac{9}{250}x=-\frac{6}{125}$$

Add \frac{6}{125} to both sides.

$$\frac{997}{250}x^{2}-\frac{9}{250}x+\frac{6}{125}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{997}{250} for a, -\frac{9}{250} for b, and \frac{6}{125} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{9}{250}\right)±\sqrt{\left(-\frac{9}{250}\right)^{2}-4\times \frac{997}{250}\times \frac{6}{125}}}{2\times \frac{997}{250}}$$

Square -\frac{9}{250} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-\frac{9}{250}\right)±\sqrt{\frac{81}{62500}-4\times \frac{997}{250}\times \frac{6}{125}}}{2\times \frac{997}{250}}$$

Multiply -4 times \frac{997}{250}.

$$x=\frac{-\left(-\frac{9}{250}\right)±\sqrt{\frac{81}{62500}-\frac{1994}{125}\times \frac{6}{125}}}{2\times \frac{997}{250}}$$

Multiply -\frac{1994}{125} times \frac{6}{125} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{9}{250}\right)±\sqrt{\frac{81}{62500}-\frac{11964}{15625}}}{2\times \frac{997}{250}}$$

Add \frac{81}{62500} to -\frac{11964}{15625} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{9}{250}\right)±\sqrt{-\frac{1911}{2500}}}{2\times \frac{997}{250}}$$

Take the square root of -\frac{1911}{2500}.

$$x=\frac{-\left(-\frac{9}{250}\right)±\frac{7\sqrt{39}i}{50}}{2\times \frac{997}{250}}$$

The opposite of -\frac{9}{250} is \frac{9}{250}.

$$x=\frac{\frac{9}{250}±\frac{7\sqrt{39}i}{50}}{2\times \frac{997}{250}}$$

Multiply 2 times \frac{997}{250}.

$$x=\frac{\frac{9}{250}±\frac{7\sqrt{39}i}{50}}{\frac{997}{125}}$$

Now solve the equation x=\frac{\frac{9}{250}±\frac{7\sqrt{39}i}{50}}{\frac{997}{125}} when ± is plus. Add \frac{9}{250} to \frac{7i\sqrt{39}}{50}.

$$x=\frac{\frac{7\sqrt{39}i}{50}+\frac{9}{250}}{\frac{997}{125}}$$

Divide \frac{9}{250}+\frac{7i\sqrt{39}}{50} by \frac{997}{125} by multiplying \frac{9}{250}+\frac{7i\sqrt{39}}{50} by the reciprocal of \frac{997}{125}.

$$x=\frac{9+35\sqrt{39}i}{1994}$$

Now solve the equation x=\frac{\frac{9}{250}±\frac{7\sqrt{39}i}{50}}{\frac{997}{125}} when ± is minus. Subtract \frac{7i\sqrt{39}}{50} from \frac{9}{250}.

$$x=\frac{-\frac{7\sqrt{39}i}{50}+\frac{9}{250}}{\frac{997}{125}}$$

Divide \frac{9}{250}-\frac{7i\sqrt{39}}{50} by \frac{997}{125} by multiplying \frac{9}{250}-\frac{7i\sqrt{39}}{50} by the reciprocal of \frac{997}{125}.

$$x=\frac{-35\sqrt{39}i+9}{1994}$$

The equation is now solved.

$$x=\frac{9+35\sqrt{39}i}{1994} x=\frac{-35\sqrt{39}i+9}{1994}$$

Steps for Completing the Square

Variable x cannot be equal to any of the values -4,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+4\right).

$$\left(2x\right)^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=1.2\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$4x^{2}=1.2\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Multiply 1.2 and \frac{1}{100} to get \frac{3}{250}.

$$4x^{2}=\frac{3}{250}\left(x-1\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{250} by x-1.

$$4x^{2}=\left(\frac{3}{250}x-\frac{3}{250}\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{250}x-\frac{3}{250} by x+4 and combine like terms.

$$4x^{2}=\frac{3}{250}x^{2}+\frac{9}{250}x-\frac{6}{125}$$

Subtract \frac{3}{250}x^{2} from both sides.

$$4x^{2}-\frac{3}{250}x^{2}=\frac{9}{250}x-\frac{6}{125}$$

Combine 4x^{2} and -\frac{3}{250}x^{2} to get \frac{997}{250}x^{2}.

$$\frac{997}{250}x^{2}=\frac{9}{250}x-\frac{6}{125}$$

Subtract \frac{9}{250}x from both sides.

$$\frac{997}{250}x^{2}-\frac{9}{250}x=-\frac{6}{125}$$

Divide both sides of the equation by \frac{997}{250}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{997}{250}x^{2}-\frac{9}{250}x}{\frac{997}{250}}=-\frac{\frac{6}{125}}{\frac{997}{250}}$$

Dividing by \frac{997}{250} undoes the multiplication by \frac{997}{250}.

$$x^{2}+\left(-\frac{\frac{9}{250}}{\frac{997}{250}}\right)x=-\frac{\frac{6}{125}}{\frac{997}{250}}$$

Divide -\frac{9}{250} by \frac{997}{250} by multiplying -\frac{9}{250} by the reciprocal of \frac{997}{250}.

$$x^{2}-\frac{9}{997}x=-\frac{\frac{6}{125}}{\frac{997}{250}}$$

Divide -\frac{6}{125} by \frac{997}{250} by multiplying -\frac{6}{125} by the reciprocal of \frac{997}{250}.

$$x^{2}-\frac{9}{997}x=-\frac{12}{997}$$

Divide -\frac{9}{997}, the coefficient of the x term, by 2 to get -\frac{9}{1994}. Then add the square of -\frac{9}{1994} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{9}{997}x+\left(-\frac{9}{1994}\right)^{2}=-\frac{12}{997}+\left(-\frac{9}{1994}\right)^{2}$$

Square -\frac{9}{1994} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{9}{997}x+\frac{81}{3976036}=-\frac{12}{997}+\frac{81}{3976036}$$

Add -\frac{12}{997} to \frac{81}{3976036} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{9}{997}x+\frac{81}{3976036}=-\frac{47775}{3976036}$$

Factor x^{2}-\frac{9}{997}x+\frac{81}{3976036}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{1994}\right)^{2}=-\frac{47775}{3976036}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{9}{1994}\right)^{2}}=\sqrt{-\frac{47775}{3976036}}$$

Simplify.

$$x-\frac{9}{1994}=\frac{35\sqrt{39}i}{1994} x-\frac{9}{1994}=-\frac{35\sqrt{39}i}{1994}$$

Add \frac{9}{1994} to both sides of the equation.

$$x=\frac{9+35\sqrt{39}i}{1994} x=\frac{-35\sqrt{39}i+9}{1994}$$