Solve (0.01-x)left(0*001-xright)=1.08/10^10

$$(0.01-x) \left( 0 \cdot 001-x \right) = \frac{ 1.08 }{ { 10 }^{ 10 } }$$

Solve for x

$$x=-\frac{\sqrt{6250027}}{500000}+0.005\approx -0.000000011$$

$$x=\frac{\sqrt{6250027}}{500000}+0.005\approx 0.010000011$$

Steps Using the Quadratic Formula

Multiply 0 and 0 to get 0.

$$\left(0.01-x\right)\left(0\times 0\times 1-x\right)=\frac{1.08}{10^{10}}$$

Multiply 0 and 0 to get 0.

$$\left(0.01-x\right)\left(0\times 1-x\right)=\frac{1.08}{10^{10}}$$

Multiply 0 and 1 to get 0.

$$\left(0.01-x\right)\left(0-x\right)=\frac{1.08}{10^{10}}$$

Anything plus zero gives itself.

$$\left(0.01-x\right)\left(-1\right)x=\frac{1.08}{10^{10}}$$

Use the distributive property to multiply 0.01-x by -1.

$$\left(-0.01+x\right)x=\frac{1.08}{10^{10}}$$

Use the distributive property to multiply -0.01+x by x.

$$-0.01x+x^{2}=\frac{1.08}{10^{10}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$-0.01x+x^{2}=\frac{1.08}{10000000000}$$

Expand \frac{1.08}{10000000000} by multiplying both numerator and the denominator by 100.

$$-0.01x+x^{2}=\frac{108}{1000000000000}$$

Reduce the fraction \frac{108}{1000000000000} to lowest terms by extracting and canceling out 4.

$$-0.01x+x^{2}=\frac{27}{250000000000}$$

Subtract \frac{27}{250000000000} from both sides.

$$-0.01x+x^{2}-\frac{27}{250000000000}=0$$

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.

$$x^{2}-0.01x-\frac{27}{250000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -0.01 for b, and -\frac{27}{250000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-0.01\right)±\sqrt{\left(-0.01\right)^{2}-4\left(-\frac{27}{250000000000}\right)}}{2}$$

Square -0.01 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-0.01\right)±\sqrt{0.0001-4\left(-\frac{27}{250000000000}\right)}}{2}$$

Multiply -4 times -\frac{27}{250000000000}.

$$x=\frac{-\left(-0.01\right)±\sqrt{0.0001+\frac{27}{62500000000}}}{2}$$

Add 0.0001 to \frac{27}{62500000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.01\right)±\sqrt{\frac{6250027}{62500000000}}}{2}$$

Take the square root of \frac{6250027}{62500000000}.

$$x=\frac{-\left(-0.01\right)±\frac{\sqrt{6250027}}{250000}}{2}$$

The opposite of -0.01 is 0.01.

$$x=\frac{0.01±\frac{\sqrt{6250027}}{250000}}{2}$$

Now solve the equation x=\frac{0.01±\frac{\sqrt{6250027}}{250000}}{2} when ± is plus. Add 0.01 to \frac{\sqrt{6250027}}{250000}.

$$x=\frac{\frac{\sqrt{6250027}}{250000}+\frac{1}{100}}{2}$$

Divide \frac{1}{100}+\frac{\sqrt{6250027}}{250000} by 2.

$$x=\frac{\sqrt{6250027}}{500000}+\frac{1}{200}$$

Now solve the equation x=\frac{0.01±\frac{\sqrt{6250027}}{250000}}{2} when ± is minus. Subtract \frac{\sqrt{6250027}}{250000} from 0.01.

$$x=\frac{-\frac{\sqrt{6250027}}{250000}+\frac{1}{100}}{2}$$

Divide \frac{1}{100}-\frac{\sqrt{6250027}}{250000} by 2.

$$x=-\frac{\sqrt{6250027}}{500000}+\frac{1}{200}$$

The equation is now solved.

$$x=\frac{\sqrt{6250027}}{500000}+\frac{1}{200} x=-\frac{\sqrt{6250027}}{500000}+\frac{1}{200}$$

Steps for Completing the Square

Multiply 0 and 0 to get 0.

$$\left(0.01-x\right)\left(0\times 0\times 1-x\right)=\frac{1.08}{10^{10}}$$

Multiply 0 and 0 to get 0.

$$\left(0.01-x\right)\left(0\times 1-x\right)=\frac{1.08}{10^{10}}$$

Multiply 0 and 1 to get 0.

$$\left(0.01-x\right)\left(0-x\right)=\frac{1.08}{10^{10}}$$

Anything plus zero gives itself.

$$\left(0.01-x\right)\left(-1\right)x=\frac{1.08}{10^{10}}$$

Use the distributive property to multiply 0.01-x by -1.

$$\left(-0.01+x\right)x=\frac{1.08}{10^{10}}$$

Use the distributive property to multiply -0.01+x by x.

$$-0.01x+x^{2}=\frac{1.08}{10^{10}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$-0.01x+x^{2}=\frac{1.08}{10000000000}$$

Expand \frac{1.08}{10000000000} by multiplying both numerator and the denominator by 100.

$$-0.01x+x^{2}=\frac{108}{1000000000000}$$

Reduce the fraction \frac{108}{1000000000000} to lowest terms by extracting and canceling out 4.

$$-0.01x+x^{2}=\frac{27}{250000000000}$$

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.

$$x^{2}-0.01x=\frac{27}{250000000000}$$

Divide -0.01, the coefficient of the x term, by 2 to get -0.005. Then add the square of -0.005 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-0.01x+\left(-0.005\right)^{2}=\frac{27}{250000000000}+\left(-0.005\right)^{2}$$

Square -0.005 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-0.01x+0.000025=\frac{27}{250000000000}+0.000025$$

Add \frac{27}{250000000000} to 0.000025 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-0.01x+0.000025=\frac{6250027}{250000000000}$$

Factor x^{2}-0.01x+0.000025. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-0.005\right)^{2}=\frac{6250027}{250000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-0.005\right)^{2}}=\sqrt{\frac{6250027}{250000000000}}$$

Simplify.

$$x-0.005=\frac{\sqrt{6250027}}{500000} x-0.005=-\frac{\sqrt{6250027}}{500000}$$

Add 0.005 to both sides of the equation.

$$x=\frac{\sqrt{6250027}}{500000}+\frac{1}{200} x=-\frac{\sqrt{6250027}}{500000}+\frac{1}{200}$$