Solve 63*10^-5=(02+x)(x)/(012-x)

$$63 \times 10 ^ { - 5 } = \frac { ( 02 + x ) ( x ) } { ( 012 - x ) }$$

Solve for x

$$x=-\frac{63}{100000}=-0.00063$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 63 and \frac{1}{100000} to get \frac{63}{100000}.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 0 and 2 to get 0.

$$\frac{63}{100000}x=-xx$$

Multiply x and x to get x^{2}.

$$\frac{63}{100000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{63}{100000}x+x^{2}=0$$

Factor out x.

$$x\left(\frac{63}{100000}+x\right)=0$$

To find equation solutions, solve x=0 and \frac{63}{100000}+x=0.

$$x=0 x=-\frac{63}{100000}$$

Variable x cannot be equal to 0.

$$x=-\frac{63}{100000}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 63 and \frac{1}{100000} to get \frac{63}{100000}.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 0 and 2 to get 0.

$$\frac{63}{100000}x=-xx$$

Multiply x and x to get x^{2}.

$$\frac{63}{100000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{63}{100000}x+x^{2}=0$$

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.

$$x^{2}+\frac{63}{100000}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{63}{100000} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{63}{100000}±\sqrt{\left(\frac{63}{100000}\right)^{2}}}{2}$$

Take the square root of \left(\frac{63}{100000}\right)^{2}.

$$x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2}$$

Now solve the equation x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2} when ± is plus. Add -\frac{63}{100000} to \frac{63}{100000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2} when ± is minus. Subtract \frac{63}{100000} from -\frac{63}{100000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{63}{50000}}{2}$$

Divide -\frac{63}{50000} by 2.

$$x=-\frac{63}{100000}$$

The equation is now solved.

$$x=0 x=-\frac{63}{100000}$$

Variable x cannot be equal to 0.

$$x=-\frac{63}{100000}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 63 and \frac{1}{100000} to get \frac{63}{100000}.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

Multiply 0 and 2 to get 0.

$$\frac{63}{100000}x=-xx$$

Multiply x and x to get x^{2}.

$$\frac{63}{100000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{63}{100000}x+x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+\frac{63}{100000}x=0$$

Divide \frac{63}{100000}, the coefficient of the x term, by 2 to get \frac{63}{200000}. Then add the square of \frac{63}{200000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{63}{100000}x+\left(\frac{63}{200000}\right)^{2}=\left(\frac{63}{200000}\right)^{2}$$

Square \frac{63}{200000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{63}{100000}x+\frac{3969}{40000000000}=\frac{3969}{40000000000}$$

Factor x^{2}+\frac{63}{100000}x+\frac{3969}{40000000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{63}{200000}\right)^{2}=\frac{3969}{40000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{63}{200000}\right)^{2}}=\sqrt{\frac{3969}{40000000000}}$$

Simplify.

$$x+\frac{63}{200000}=\frac{63}{200000} x+\frac{63}{200000}=-\frac{63}{200000}$$

Subtract \frac{63}{200000} from both sides of the equation.

$$x=0 x=-\frac{63}{100000}$$

Variable x cannot be equal to 0.

$$x=-\frac{63}{100000}$$