x^2+x/(20)+1/1250 =0

Solution

x^{2} + \frac{x}{20} + \frac{1}{1250} = 0

x = - \frac{1}{40} + i \frac{7}{200}, x = - \frac{1}{40} - i \frac{7}{200}

Solution steps

x^{2} + \frac{x}{20} + \frac{1}{1250} = 0

Find Least Common Multiplier of

20, 1250 : 2500

Multiply by LCM=

2500

x^{2} \cdot 2500 + \frac{x}{20} \cdot 2500 + \frac{1}{1250} \cdot 2500 = 0 \cdot 2500

Simplify

2500 x^{2} + 125 x + 2 = 0

Divide both sides by

2500

\frac{2500 x ^{2}}{2500} + \frac{125 x}{2500} + \frac{2}{2500} = \frac{0}{2500}

Write in the standard form

a x^{2} + b x + c = 0

x^{2} + \frac{1 \cdot x}{20} + \frac{1}{1250} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- \frac{1}{20} \pm ( \frac{1}{20} ) ^{2} - 4 \cdot 1 \cdot \frac{1}{1250}}{2 \cdot 1}

Simplify

(\frac{1}{20})^{2} - 4 \cdot 1 \cdot \frac{1}{1250} : i \frac{7}{100}

x_{1, 2} = \frac{- \frac{1}{20} \pm i \frac{7}{100}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- \frac{1}{20} + i \frac{7}{100}}{2 \cdot 1}, x_{2} = \frac{- \frac{1}{20} - i \frac{7}{100}}{2 \cdot 1}

x = \frac{- \frac{1}{20} + i \frac{7}{100}}{2 \cdot 1} : - \frac{1}{40} + i \frac{7}{200}

x = \frac{- \frac{1}{20} - i \frac{7}{100}}{2 \cdot 1} : - \frac{1}{40} - i \frac{7}{200}

The solutions to the quadratic equation are:

x = - \frac{1}{40} + i \frac{7}{200}, x = - \frac{1}{40} - i \frac{7}{200}

13 = \frac{5 x ^{2}}{2 ( 32.2 )} - 20 + 4 (0.1 x)^{2}

2 (x - 2)^{2} = 0

3 x^{2} + 15 - 15 = 15

\frac{1}{4} x^{2} + 4 x + 16 = 0