Solve 0.08x^2div(1-x)=2.5*10^-5

$$0.08 { x }^{ 2 } \div (1-x)=2.5 \times { 10 }^{ -5 }$$

Solve for x

$$x=\frac{\sqrt{12801}-1}{6400}\approx 0.01752211$$

$$x=\frac{-\sqrt{12801}-1}{6400}\approx -0.01783461$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by -x+1.

$$0.08x^{2}=2.5\times 10^{-5}\left(-x+1\right)$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$0.08x^{2}=2.5\times \frac{1}{100000}\left(-x+1\right)$$

Multiply 2.5 and \frac{1}{100000} to get \frac{1}{40000}.

$$0.08x^{2}=\frac{1}{40000}\left(-x+1\right)$$

Use the distributive property to multiply \frac{1}{40000} by -x+1.

$$0.08x^{2}=-\frac{1}{40000}x+\frac{1}{40000}$$

Add \frac{1}{40000}x to both sides.

$$0.08x^{2}+\frac{1}{40000}x=\frac{1}{40000}$$

Subtract \frac{1}{40000} from both sides.

$$0.08x^{2}+\frac{1}{40000}x-\frac{1}{40000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.08 for a, \frac{1}{40000} for b, and -\frac{1}{40000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{1}{40000}±\sqrt{\left(\frac{1}{40000}\right)^{2}-4\times 0.08\left(-\frac{1}{40000}\right)}}{2\times 0.08}$$

Square \frac{1}{40000} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{1}{40000}±\sqrt{\frac{1}{1600000000}-4\times 0.08\left(-\frac{1}{40000}\right)}}{2\times 0.08}$$

Multiply -4 times 0.08.

$$x=\frac{-\frac{1}{40000}±\sqrt{\frac{1}{1600000000}-0.32\left(-\frac{1}{40000}\right)}}{2\times 0.08}$$

Multiply -0.32 times -\frac{1}{40000} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{1}{40000}±\sqrt{\frac{1}{1600000000}+\frac{1}{125000}}}{2\times 0.08}$$

Add \frac{1}{1600000000} to \frac{1}{125000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{1}{40000}±\sqrt{\frac{12801}{1600000000}}}{2\times 0.08}$$

Take the square root of \frac{12801}{1600000000}.

$$x=\frac{-\frac{1}{40000}±\frac{\sqrt{12801}}{40000}}{2\times 0.08}$$

Multiply 2 times 0.08.

$$x=\frac{-\frac{1}{40000}±\frac{\sqrt{12801}}{40000}}{0.16}$$

Now solve the equation x=\frac{-\frac{1}{40000}±\frac{\sqrt{12801}}{40000}}{0.16} when ± is plus. Add -\frac{1}{40000} to \frac{\sqrt{12801}}{40000}.

$$x=\frac{\sqrt{12801}-1}{0.16\times 40000}$$

Divide \frac{-1+\sqrt{12801}}{40000} by 0.16 by multiplying \frac{-1+\sqrt{12801}}{40000} by the reciprocal of 0.16.

$$x=\frac{\sqrt{12801}-1}{6400}$$

Now solve the equation x=\frac{-\frac{1}{40000}±\frac{\sqrt{12801}}{40000}}{0.16} when ± is minus. Subtract \frac{\sqrt{12801}}{40000} from -\frac{1}{40000}.

$$x=\frac{-\sqrt{12801}-1}{0.16\times 40000}$$

Divide \frac{-1-\sqrt{12801}}{40000} by 0.16 by multiplying \frac{-1-\sqrt{12801}}{40000} by the reciprocal of 0.16.

$$x=\frac{-\sqrt{12801}-1}{6400}$$

The equation is now solved.

$$x=\frac{\sqrt{12801}-1}{6400} x=\frac{-\sqrt{12801}-1}{6400}$$

Steps for Completing the Square

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by -x+1.

$$0.08x^{2}=2.5\times 10^{-5}\left(-x+1\right)$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$0.08x^{2}=2.5\times \frac{1}{100000}\left(-x+1\right)$$

Multiply 2.5 and \frac{1}{100000} to get \frac{1}{40000}.

$$0.08x^{2}=\frac{1}{40000}\left(-x+1\right)$$

Use the distributive property to multiply \frac{1}{40000} by -x+1.

$$0.08x^{2}=-\frac{1}{40000}x+\frac{1}{40000}$$

Add \frac{1}{40000}x to both sides.

$$0.08x^{2}+\frac{1}{40000}x=\frac{1}{40000}$$

Divide both sides of the equation by 0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.08x^{2}+\frac{1}{40000}x}{0.08}=\frac{\frac{1}{40000}}{0.08}$$

Dividing by 0.08 undoes the multiplication by 0.08.

$$x^{2}+\frac{\frac{1}{40000}}{0.08}x=\frac{\frac{1}{40000}}{0.08}$$

Divide \frac{1}{40000} by 0.08 by multiplying \frac{1}{40000} by the reciprocal of 0.08.

$$x^{2}+\frac{1}{3200}x=\frac{\frac{1}{40000}}{0.08}$$

Divide \frac{1}{40000} by 0.08 by multiplying \frac{1}{40000} by the reciprocal of 0.08.

$$x^{2}+\frac{1}{3200}x=\frac{1}{3200}$$

Divide \frac{1}{3200}, the coefficient of the x term, by 2 to get \frac{1}{6400}. Then add the square of \frac{1}{6400} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1}{3200}x+\left(\frac{1}{6400}\right)^{2}=\frac{1}{3200}+\left(\frac{1}{6400}\right)^{2}$$

Square \frac{1}{6400} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1}{3200}x+\frac{1}{40960000}=\frac{1}{3200}+\frac{1}{40960000}$$

Add \frac{1}{3200} to \frac{1}{40960000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{1}{3200}x+\frac{1}{40960000}=\frac{12801}{40960000}$$

Factor x^{2}+\frac{1}{3200}x+\frac{1}{40960000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{6400}\right)^{2}=\frac{12801}{40960000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{6400}\right)^{2}}=\sqrt{\frac{12801}{40960000}}$$

Simplify.

$$x+\frac{1}{6400}=\frac{\sqrt{12801}}{6400} x+\frac{1}{6400}=-\frac{\sqrt{12801}}{6400}$$

Subtract \frac{1}{6400} from both sides of the equation.

$$x=\frac{\sqrt{12801}-1}{6400} x=\frac{-\sqrt{12801}-1}{6400}$$