Solve (2x)^2/(1-x)(1-5-x)=12*10^-2

$$\frac { ( 2 x ) ^ { 2 } } { ( 1 - x ) ( 1 - 5 - x ) } = 12 \times 10 ^ { - 2 }$$

Solve for x (complex solution)

$$x=\frac{9+5\sqrt{183}i}{194}\approx 0.046391753+0.348653331i$$

$$x=\frac{-5\sqrt{183}i+9}{194}\approx 0.046391753-0.348653331i$$

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).

$$\left(2x\right)^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

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

$$2^{2}x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

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

$$4x^{2}=12\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Multiply 12 and \frac{1}{100} to get \frac{3}{25}.

$$4x^{2}=\frac{3}{25}\left(x-1\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{25} by x-1.

$$4x^{2}=\left(\frac{3}{25}x-\frac{3}{25}\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{25}x-\frac{3}{25} by x+4 and combine like terms.

$$4x^{2}=\frac{3}{25}x^{2}+\frac{9}{25}x-\frac{12}{25}$$

Subtract \frac{3}{25}x^{2} from both sides.

$$4x^{2}-\frac{3}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Combine 4x^{2} and -\frac{3}{25}x^{2} to get \frac{97}{25}x^{2}.

$$\frac{97}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Subtract \frac{9}{25}x from both sides.

$$\frac{97}{25}x^{2}-\frac{9}{25}x=-\frac{12}{25}$$

Add \frac{12}{25} to both sides.

$$\frac{97}{25}x^{2}-\frac{9}{25}x+\frac{12}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{97}{25} for a, -\frac{9}{25} for b, and \frac{12}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\left(-\frac{9}{25}\right)^{2}-4\times \frac{97}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Square -\frac{9}{25} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81}{625}-4\times \frac{97}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Multiply -4 times \frac{97}{25}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81}{625}-\frac{388}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Multiply -\frac{388}{25} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81-4656}{625}}}{2\times \frac{97}{25}}$$

Add \frac{81}{625} to -\frac{4656}{625} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{-\frac{183}{25}}}{2\times \frac{97}{25}}$$

Take the square root of -\frac{183}{25}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\frac{\sqrt{183}i}{5}}{2\times \frac{97}{25}}$$

The opposite of -\frac{9}{25} is \frac{9}{25}.

$$x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{2\times \frac{97}{25}}$$

Multiply 2 times \frac{97}{25}.

$$x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}}$$

Now solve the equation x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}} when ± is plus. Add \frac{9}{25} to \frac{i\sqrt{183}}{5}.

$$x=\frac{\frac{\sqrt{183}i}{5}+\frac{9}{25}}{\frac{194}{25}}$$

Divide \frac{9}{25}+\frac{i\sqrt{183}}{5} by \frac{194}{25} by multiplying \frac{9}{25}+\frac{i\sqrt{183}}{5} by the reciprocal of \frac{194}{25}.

$$x=\frac{9+5\sqrt{183}i}{194}$$

Now solve the equation x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}} when ± is minus. Subtract \frac{i\sqrt{183}}{5} from \frac{9}{25}.

$$x=\frac{-\frac{\sqrt{183}i}{5}+\frac{9}{25}}{\frac{194}{25}}$$

Divide \frac{9}{25}-\frac{i\sqrt{183}}{5} by \frac{194}{25} by multiplying \frac{9}{25}-\frac{i\sqrt{183}}{5} by the reciprocal of \frac{194}{25}.

$$x=\frac{-5\sqrt{183}i+9}{194}$$

The equation is now solved.

$$x=\frac{9+5\sqrt{183}i}{194} x=\frac{-5\sqrt{183}i+9}{194}$$

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).

$$\left(2x\right)^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

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

$$2^{2}x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

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

$$4x^{2}=12\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Multiply 12 and \frac{1}{100} to get \frac{3}{25}.

$$4x^{2}=\frac{3}{25}\left(x-1\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{25} by x-1.

$$4x^{2}=\left(\frac{3}{25}x-\frac{3}{25}\right)\left(x+4\right)$$

Use the distributive property to multiply \frac{3}{25}x-\frac{3}{25} by x+4 and combine like terms.

$$4x^{2}=\frac{3}{25}x^{2}+\frac{9}{25}x-\frac{12}{25}$$

Subtract \frac{3}{25}x^{2} from both sides.

$$4x^{2}-\frac{3}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Combine 4x^{2} and -\frac{3}{25}x^{2} to get \frac{97}{25}x^{2}.

$$\frac{97}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Subtract \frac{9}{25}x from both sides.

$$\frac{97}{25}x^{2}-\frac{9}{25}x=-\frac{12}{25}$$

Divide both sides of the equation by \frac{97}{25}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{97}{25}x^{2}-\frac{9}{25}x}{\frac{97}{25}}=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Dividing by \frac{97}{25} undoes the multiplication by \frac{97}{25}.

$$x^{2}+\left(-\frac{\frac{9}{25}}{\frac{97}{25}}\right)x=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Divide -\frac{9}{25} by \frac{97}{25} by multiplying -\frac{9}{25} by the reciprocal of \frac{97}{25}.

$$x^{2}-\frac{9}{97}x=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Divide -\frac{12}{25} by \frac{97}{25} by multiplying -\frac{12}{25} by the reciprocal of \frac{97}{25}.

$$x^{2}-\frac{9}{97}x=-\frac{12}{97}$$

Divide -\frac{9}{97}, the coefficient of the x term, by 2 to get -\frac{9}{194}. Then add the square of -\frac{9}{194} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{9}{97}x+\left(-\frac{9}{194}\right)^{2}=-\frac{12}{97}+\left(-\frac{9}{194}\right)^{2}$$

Square -\frac{9}{194} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{9}{97}x+\frac{81}{37636}=-\frac{12}{97}+\frac{81}{37636}$$

Add -\frac{12}{97} to \frac{81}{37636} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{9}{97}x+\frac{81}{37636}=-\frac{4575}{37636}$$

Factor x^{2}-\frac{9}{97}x+\frac{81}{37636}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{194}\right)^{2}=-\frac{4575}{37636}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{9}{194}\right)^{2}}=\sqrt{-\frac{4575}{37636}}$$

Simplify.

$$x-\frac{9}{194}=\frac{5\sqrt{183}i}{194} x-\frac{9}{194}=-\frac{5\sqrt{183}i}{194}$$

Add \frac{9}{194} to both sides of the equation.

$$x=\frac{9+5\sqrt{183}i}{194} x=\frac{-5\sqrt{183}i+9}{194}$$