Solve 62.44/33.73=(1-x)^2/(1-x^2)

$$\frac { 62.44 } { 33.73 } = \frac { ( 1 - x ) ^ { 2 } } { ( 1 - x ^ { 2 } ) }$$

Solve for x

$$x=-\frac{2871}{9617}\approx -0.298533846$$

Steps Using the Quadratic Formula

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

$$\left(x-1\right)\left(-x-1\right)\times \frac{62.44}{33.73}=\left(1-x\right)^{2}$$

Use the distributive property to multiply x-1 by -x-1 and combine like terms.

$$\left(-x^{2}+1\right)\times \frac{62.44}{33.73}=\left(1-x\right)^{2}$$

Expand \frac{62.44}{33.73} by multiplying both numerator and the denominator by 100.

$$\left(-x^{2}+1\right)\times \frac{6244}{3373}=\left(1-x\right)^{2}$$

Use the distributive property to multiply -x^{2}+1 by \frac{6244}{3373}.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}=\left(1-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}=1-2x+x^{2}$$

Subtract 1 from both sides.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}-1=-2x+x^{2}$$

Subtract 1 from \frac{6244}{3373} to get \frac{2871}{3373}.

$$-\frac{6244}{3373}x^{2}+\frac{2871}{3373}=-2x+x^{2}$$

Add 2x to both sides.

$$-\frac{6244}{3373}x^{2}+\frac{2871}{3373}+2x=x^{2}$$

Subtract x^{2} from both sides.

$$-\frac{6244}{3373}x^{2}+\frac{2871}{3373}+2x-x^{2}=0$$

Combine -\frac{6244}{3373}x^{2} and -x^{2} to get -\frac{9617}{3373}x^{2}.

$$-\frac{9617}{3373}x^{2}+\frac{2871}{3373}+2x=0$$

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.

$$-\frac{9617}{3373}x^{2}+2x+\frac{2871}{3373}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{9617}{3373} for a, 2 for b, and \frac{2871}{3373} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-\frac{9617}{3373}\right)\times \frac{2871}{3373}}}{2\left(-\frac{9617}{3373}\right)}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-\frac{9617}{3373}\right)\times \frac{2871}{3373}}}{2\left(-\frac{9617}{3373}\right)}$$

Multiply -4 times -\frac{9617}{3373}.

$$x=\frac{-2±\sqrt{4+\frac{38468}{3373}\times \frac{2871}{3373}}}{2\left(-\frac{9617}{3373}\right)}$$

Multiply \frac{38468}{3373} times \frac{2871}{3373} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-2±\sqrt{4+\frac{110441628}{11377129}}}{2\left(-\frac{9617}{3373}\right)}$$

Add 4 to \frac{110441628}{11377129}.

$$x=\frac{-2±\sqrt{\frac{155950144}{11377129}}}{2\left(-\frac{9617}{3373}\right)}$$

Take the square root of \frac{155950144}{11377129}.

$$x=\frac{-2±\frac{12488}{3373}}{2\left(-\frac{9617}{3373}\right)}$$

Multiply 2 times -\frac{9617}{3373}.

$$x=\frac{-2±\frac{12488}{3373}}{-\frac{19234}{3373}}$$

Now solve the equation x=\frac{-2±\frac{12488}{3373}}{-\frac{19234}{3373}} when ± is plus. Add -2 to \frac{12488}{3373}.

$$x=\frac{\frac{5742}{3373}}{-\frac{19234}{3373}}$$

Divide \frac{5742}{3373} by -\frac{19234}{3373} by multiplying \frac{5742}{3373} by the reciprocal of -\frac{19234}{3373}.

$$x=-\frac{2871}{9617}$$

Now solve the equation x=\frac{-2±\frac{12488}{3373}}{-\frac{19234}{3373}} when ± is minus. Subtract \frac{12488}{3373} from -2.

$$x=-\frac{\frac{19234}{3373}}{-\frac{19234}{3373}}$$

Divide -\frac{19234}{3373} by -\frac{19234}{3373} by multiplying -\frac{19234}{3373} by the reciprocal of -\frac{19234}{3373}.

$$x=1$$

The equation is now solved.

$$x=-\frac{2871}{9617} x=1$$

Variable x cannot be equal to 1.

$$x=-\frac{2871}{9617}$$

Steps for Completing the Square

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

$$\left(x-1\right)\left(-x-1\right)\times \frac{62.44}{33.73}=\left(1-x\right)^{2}$$

Use the distributive property to multiply x-1 by -x-1 and combine like terms.

$$\left(-x^{2}+1\right)\times \frac{62.44}{33.73}=\left(1-x\right)^{2}$$

Expand \frac{62.44}{33.73} by multiplying both numerator and the denominator by 100.

$$\left(-x^{2}+1\right)\times \frac{6244}{3373}=\left(1-x\right)^{2}$$

Use the distributive property to multiply -x^{2}+1 by \frac{6244}{3373}.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}=\left(1-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}=1-2x+x^{2}$$

Add 2x to both sides.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}+2x=1+x^{2}$$

Subtract x^{2} from both sides.

$$-\frac{6244}{3373}x^{2}+\frac{6244}{3373}+2x-x^{2}=1$$

Combine -\frac{6244}{3373}x^{2} and -x^{2} to get -\frac{9617}{3373}x^{2}.

$$-\frac{9617}{3373}x^{2}+\frac{6244}{3373}+2x=1$$

Subtract \frac{6244}{3373} from both sides.

$$-\frac{9617}{3373}x^{2}+2x=1-\frac{6244}{3373}$$

Subtract \frac{6244}{3373} from 1 to get -\frac{2871}{3373}.

$$-\frac{9617}{3373}x^{2}+2x=-\frac{2871}{3373}$$

Divide both sides of the equation by -\frac{9617}{3373}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{9617}{3373}x^{2}+2x}{-\frac{9617}{3373}}=-\frac{\frac{2871}{3373}}{-\frac{9617}{3373}}$$

Dividing by -\frac{9617}{3373} undoes the multiplication by -\frac{9617}{3373}.

$$x^{2}+\frac{2}{-\frac{9617}{3373}}x=-\frac{\frac{2871}{3373}}{-\frac{9617}{3373}}$$

Divide 2 by -\frac{9617}{3373} by multiplying 2 by the reciprocal of -\frac{9617}{3373}.

$$x^{2}-\frac{6746}{9617}x=-\frac{\frac{2871}{3373}}{-\frac{9617}{3373}}$$

Divide -\frac{2871}{3373} by -\frac{9617}{3373} by multiplying -\frac{2871}{3373} by the reciprocal of -\frac{9617}{3373}.

$$x^{2}-\frac{6746}{9617}x=\frac{2871}{9617}$$

Divide -\frac{6746}{9617}, the coefficient of the x term, by 2 to get -\frac{3373}{9617}. Then add the square of -\frac{3373}{9617} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{6746}{9617}x+\left(-\frac{3373}{9617}\right)^{2}=\frac{2871}{9617}+\left(-\frac{3373}{9617}\right)^{2}$$

Square -\frac{3373}{9617} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{6746}{9617}x+\frac{11377129}{92486689}=\frac{2871}{9617}+\frac{11377129}{92486689}$$

Add \frac{2871}{9617} to \frac{11377129}{92486689} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{6746}{9617}x+\frac{11377129}{92486689}=\frac{38987536}{92486689}$$

Factor x^{2}-\frac{6746}{9617}x+\frac{11377129}{92486689}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3373}{9617}\right)^{2}=\frac{38987536}{92486689}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{3373}{9617}\right)^{2}}=\sqrt{\frac{38987536}{92486689}}$$

Simplify.

$$x-\frac{3373}{9617}=\frac{6244}{9617} x-\frac{3373}{9617}=-\frac{6244}{9617}$$

Add \frac{3373}{9617} to both sides of the equation.

$$x=1 x=-\frac{2871}{9617}$$

Variable x cannot be equal to 1.

$$x=-\frac{2871}{9617}$$