Solve x^2-5*10^-5(x)+4*10^-10=0

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

Solve for x

$$x=\frac{1}{100000}=0.00001$$

$$x=\frac{1}{25000}=0.00004$$

Steps Using the Quadratic Formula

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

$$x^{2}-5\times \frac{1}{100000}x+4\times 10^{-10}=0$$

Multiply 5 and \frac{1}{100000} to get \frac{1}{20000}.

$$x^{2}-\frac{1}{20000}x+4\times 10^{-10}=0$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$x^{2}-\frac{1}{20000}x+4\times \frac{1}{10000000000}=0$$

Multiply 4 and \frac{1}{10000000000} to get \frac{1}{2500000000}.

$$x^{2}-\frac{1}{20000}x+\frac{1}{2500000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -\frac{1}{20000} for b, and \frac{1}{2500000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{20000}\right)±\sqrt{\left(-\frac{1}{20000}\right)^{2}-4\times \frac{1}{2500000000}}}{2}$$

Square -\frac{1}{20000} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-\frac{1}{20000}\right)±\sqrt{\frac{1}{400000000}-4\times \frac{1}{2500000000}}}{2}$$

Multiply -4 times \frac{1}{2500000000}.

$$x=\frac{-\left(-\frac{1}{20000}\right)±\sqrt{\frac{1}{400000000}-\frac{1}{625000000}}}{2}$$

Add \frac{1}{400000000} to -\frac{1}{625000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-\frac{1}{20000}\right)±\sqrt{\frac{9}{10000000000}}}{2}$$

Take the square root of \frac{9}{10000000000}.

$$x=\frac{-\left(-\frac{1}{20000}\right)±\frac{3}{100000}}{2}$$

The opposite of -\frac{1}{20000} is \frac{1}{20000}.

$$x=\frac{\frac{1}{20000}±\frac{3}{100000}}{2}$$

Now solve the equation x=\frac{\frac{1}{20000}±\frac{3}{100000}}{2} when ± is plus. Add \frac{1}{20000} to \frac{3}{100000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{1}{12500}}{2}$$

Divide \frac{1}{12500} by 2.

$$x=\frac{1}{25000}$$

Now solve the equation x=\frac{\frac{1}{20000}±\frac{3}{100000}}{2} when ± is minus. Subtract \frac{3}{100000} from \frac{1}{20000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{1}{50000}}{2}$$

Divide \frac{1}{50000} by 2.

$$x=\frac{1}{100000}$$

The equation is now solved.

$$x=\frac{1}{25000} x=\frac{1}{100000}$$

Steps for Completing the Square

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

$$x^{2}-5\times \frac{1}{100000}x+4\times 10^{-10}=0$$

Multiply 5 and \frac{1}{100000} to get \frac{1}{20000}.

$$x^{2}-\frac{1}{20000}x+4\times 10^{-10}=0$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$x^{2}-\frac{1}{20000}x+4\times \frac{1}{10000000000}=0$$

Multiply 4 and \frac{1}{10000000000} to get \frac{1}{2500000000}.

$$x^{2}-\frac{1}{20000}x+\frac{1}{2500000000}=0$$

Subtract \frac{1}{2500000000} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-\frac{1}{20000}x=-\frac{1}{2500000000}$$

Divide -\frac{1}{20000}, the coefficient of the x term, by 2 to get -\frac{1}{40000}. Then add the square of -\frac{1}{40000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{20000}x+\left(-\frac{1}{40000}\right)^{2}=-\frac{1}{2500000000}+\left(-\frac{1}{40000}\right)^{2}$$

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

$$x^{2}-\frac{1}{20000}x+\frac{1}{1600000000}=-\frac{1}{2500000000}+\frac{1}{1600000000}$$

Add -\frac{1}{2500000000} to \frac{1}{1600000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{1}{20000}x+\frac{1}{1600000000}=\frac{9}{40000000000}$$

Factor x^{2}-\frac{1}{20000}x+\frac{1}{1600000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{40000}\right)^{2}=\frac{9}{40000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{40000}\right)^{2}}=\sqrt{\frac{9}{40000000000}}$$

Simplify.

$$x-\frac{1}{40000}=\frac{3}{200000} x-\frac{1}{40000}=-\frac{3}{200000}$$

Add \frac{1}{40000} to both sides of the equation.

$$x=\frac{1}{25000} x=\frac{1}{100000}$$