0.03x^2-0.4x+0.07=0

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Solution for 0.03x^2-0.4x+0.07=0 equation: 


Simplifying
0.03x2 + -0.4x + 0.07 = 0

Reorder the terms:
0.07 + -0.4x + 0.03x2 = 0

Solving
0.07 + -0.4x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
2.333333333 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -13.33333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -13.33333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -13.33333333x + x2 = 0 + -2.333333333
-13.33333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-13.33333333x + x2 = -2.333333333

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = -2.333333333 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -2.333333333 + 44.44444442

Combine like terms: -2.333333333 + 44.44444442 = 42.111111087
44.44444442 + -13.33333333x + x2 = 42.111111087

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 42.111111087

Calculate the square root of the right side: 6.489307443

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 6.489307443 and -6.489307443.


Subproblem 1
x + -6.666666665 = 6.489307443

Simplifying
x + -6.666666665 = 6.489307443

Reorder the terms:
-6.666666665 + x = 6.489307443

Solving
-6.666666665 + x = 6.489307443

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 6.489307443 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 6.489307443 + 6.666666665
x = 6.489307443 + 6.666666665

Combine like terms: 6.489307443 + 6.666666665 = 13.155974108
x = 13.155974108

Simplifying
x = 13.155974108


Subproblem 2
x + -6.666666665 = -6.489307443

Simplifying
x + -6.666666665 = -6.489307443

Reorder the terms:
-6.666666665 + x = -6.489307443

Solving
-6.666666665 + x = -6.489307443

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -6.489307443 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -6.489307443 + 6.666666665
x = -6.489307443 + 6.666666665

Combine like terms: -6.489307443 + 6.666666665 = 0.177359222
x = 0.177359222

Simplifying
x = 0.177359222


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.155974108, 0.177359222}

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