2x^2+0.1x=0.04

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Solution for 2x^2+0.1x=0.04 equation: 


Simplifying
2x2 + 0.1x = 0.04

Reorder the terms:
0.1x + 2x2 = 0.04

Solving
0.1x + 2x2 = 0.04

Solving for variable 'x'.

Reorder the terms:
-0.04 + 0.1x + 2x2 = 0.04 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
-0.04 + 0.1x + 2x2 = 0.00

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.02 + 0.05x + x2 = 0.00

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + 0.05x + 0.02 + x2 = 0.00 + 0.02

Reorder the terms:
-0.02 + 0.02 + 0.05x + x2 = 0.00 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + 0.05x + x2 = 0.00 + 0.02
0.05x + x2 = 0.00 + 0.02

Combine like terms: 0.00 + 0.02 = 0.02
0.05x + x2 = 0.02

The x term is 0.05x.  Take half its coefficient (0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
0.05x + 0.000625 + x2 = 0.02 + 0.000625

Reorder the terms:
0.000625 + 0.05x + x2 = 0.02 + 0.000625

Combine like terms: 0.02 + 0.000625 = 0.020625
0.000625 + 0.05x + x2 = 0.020625

Factor a perfect square on the left side:
(x + 0.025)(x + 0.025) = 0.020625

Calculate the square root of the right side: 0.143614066

Break this problem into two subproblems by setting 
(x + 0.025) equal to 0.143614066 and -0.143614066.


Subproblem 1
x + 0.025 = 0.143614066

Simplifying
x + 0.025 = 0.143614066

Reorder the terms:
0.025 + x = 0.143614066

Solving
0.025 + x = 0.143614066

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = 0.143614066 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = 0.143614066 + -0.025
x = 0.143614066 + -0.025

Combine like terms: 0.143614066 + -0.025 = 0.118614066
x = 0.118614066

Simplifying
x = 0.118614066


Subproblem 2
x + 0.025 = -0.143614066

Simplifying
x + 0.025 = -0.143614066

Reorder the terms:
0.025 + x = -0.143614066

Solving
0.025 + x = -0.143614066

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.025' to each side of the equation.
0.025 + -0.025 + x = -0.143614066 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + x = -0.143614066 + -0.025
x = -0.143614066 + -0.025

Combine like terms: -0.143614066 + -0.025 = -0.168614066
x = -0.168614066

Simplifying
x = -0.168614066


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.118614066, -0.168614066}

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