Solve 0,092x^2/5(1-x)=5.2x10^-4

$$\frac { 0,092 x ^ { 2 } } { 5 ( 1 - x ) } = 5.2 x 10 ^ { - 4 }$$

Solve for x

$$x=0$$

Steps Using Factoring

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 5\left(-x+1\right).

$$0\times 0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 0 to get 0.

$$0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 92 to get 0.

$$0x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Anything times zero gives zero.

$$0=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$0=5.2x\times \frac{1}{10000}\times 5\left(-x+1\right)$$

Multiply 5.2 and \frac{1}{10000} to get \frac{13}{25000}.

$$0=\frac{13}{25000}x\times 5\left(-x+1\right)$$

Multiply \frac{13}{25000} and 5 to get \frac{13}{5000}.

$$0=\frac{13}{5000}x\left(-x+1\right)$$

Use the distributive property to multiply \frac{13}{5000}x by -x+1.

$$0=-\frac{13}{5000}x^{2}+\frac{13}{5000}x$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{13}{5000}x^{2}+\frac{13}{5000}x=0$$

Factor out x.

$$x\left(-\frac{13}{5000}x+\frac{13}{5000}\right)=0$$

To find equation solutions, solve x=0 and \frac{-13x+13}{5000}=0.

$$x=0 x=1$$

Variable x cannot be equal to 1.

$$x=0$$

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 5\left(-x+1\right).

$$0\times 0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 0 to get 0.

$$0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 92 to get 0.

$$0x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Anything times zero gives zero.

$$0=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$0=5.2x\times \frac{1}{10000}\times 5\left(-x+1\right)$$

Multiply 5.2 and \frac{1}{10000} to get \frac{13}{25000}.

$$0=\frac{13}{25000}x\times 5\left(-x+1\right)$$

Multiply \frac{13}{25000} and 5 to get \frac{13}{5000}.

$$0=\frac{13}{5000}x\left(-x+1\right)$$

Use the distributive property to multiply \frac{13}{5000}x by -x+1.

$$0=-\frac{13}{5000}x^{2}+\frac{13}{5000}x$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{13}{5000}x^{2}+\frac{13}{5000}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{13}{5000} for a, \frac{13}{5000} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{13}{5000}±\sqrt{\left(\frac{13}{5000}\right)^{2}}}{2\left(-\frac{13}{5000}\right)}$$

Take the square root of \left(\frac{13}{5000}\right)^{2}.

$$x=\frac{-\frac{13}{5000}±\frac{13}{5000}}{2\left(-\frac{13}{5000}\right)}$$

Multiply 2 times -\frac{13}{5000}.

$$x=\frac{-\frac{13}{5000}±\frac{13}{5000}}{-\frac{13}{2500}}$$

Now solve the equation x=\frac{-\frac{13}{5000}±\frac{13}{5000}}{-\frac{13}{2500}} when ± is plus. Add -\frac{13}{5000} to \frac{13}{5000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-\frac{13}{2500}}$$

Divide 0 by -\frac{13}{2500} by multiplying 0 by the reciprocal of -\frac{13}{2500}.

$$x=0$$

Now solve the equation x=\frac{-\frac{13}{5000}±\frac{13}{5000}}{-\frac{13}{2500}} when ± is minus. Subtract \frac{13}{5000} from -\frac{13}{5000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{13}{2500}}{-\frac{13}{2500}}$$

Divide -\frac{13}{2500} by -\frac{13}{2500} by multiplying -\frac{13}{2500} by the reciprocal of -\frac{13}{2500}.

$$x=1$$

The equation is now solved.

$$x=0 x=1$$

Variable x cannot be equal to 1.

$$x=0$$

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 5\left(-x+1\right).

$$0\times 0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 0 to get 0.

$$0\times 92x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Multiply 0 and 92 to get 0.

$$0x^{2}=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Anything times zero gives zero.

$$0=5.2x\times 10^{-4}\times 5\left(-x+1\right)$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$0=5.2x\times \frac{1}{10000}\times 5\left(-x+1\right)$$

Multiply 5.2 and \frac{1}{10000} to get \frac{13}{25000}.

$$0=\frac{13}{25000}x\times 5\left(-x+1\right)$$

Multiply \frac{13}{25000} and 5 to get \frac{13}{5000}.

$$0=\frac{13}{5000}x\left(-x+1\right)$$

Use the distributive property to multiply \frac{13}{5000}x by -x+1.

$$0=-\frac{13}{5000}x^{2}+\frac{13}{5000}x$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{13}{5000}x^{2}+\frac{13}{5000}x=0$$

Divide both sides of the equation by -\frac{13}{5000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{13}{5000}x^{2}+\frac{13}{5000}x}{-\frac{13}{5000}}=\frac{0}{-\frac{13}{5000}}$$

Dividing by -\frac{13}{5000} undoes the multiplication by -\frac{13}{5000}.

$$x^{2}+\frac{\frac{13}{5000}}{-\frac{13}{5000}}x=\frac{0}{-\frac{13}{5000}}$$

Divide \frac{13}{5000} by -\frac{13}{5000} by multiplying \frac{13}{5000} by the reciprocal of -\frac{13}{5000}.

$$x^{2}-x=\frac{0}{-\frac{13}{5000}}$$

Divide 0 by -\frac{13}{5000} by multiplying 0 by the reciprocal of -\frac{13}{5000}.

$$x^{2}-x=0$$

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

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-x+\frac{1}{4}=\frac{1}{4}$$

Factor x^{2}-x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x-\frac{1}{2}=\frac{1}{2} x-\frac{1}{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$x=1 x=0$$

Variable x cannot be equal to 1.

$$x=0$$