0.04x^2-0.5x+0.06=0

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Solution for 0.04x^2-0.5x+0.06=0 equation: 


Simplifying
0.04x2 + -0.5x + 0.06 = 0

Reorder the terms:
0.06 + -0.5x + 0.04x2 = 0

Solving
0.06 + -0.5x + 0.04x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.04'.
1.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -12.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -12.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -12.5x + x2 = 0 + -1.5
-12.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-12.5x + x2 = -1.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -1.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -1.5 + 39.0625

Combine like terms: -1.5 + 39.0625 = 37.5625
39.0625 + -12.5x + x2 = 37.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 37.5625

Calculate the square root of the right side: 6.128825336

Break this problem into two subproblems by setting 
(x + -6.25) equal to 6.128825336 and -6.128825336.


Subproblem 1
x + -6.25 = 6.128825336

Simplifying
x + -6.25 = 6.128825336

Reorder the terms:
-6.25 + x = 6.128825336

Solving
-6.25 + x = 6.128825336

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 6.128825336 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 6.128825336 + 6.25
x = 6.128825336 + 6.25

Combine like terms: 6.128825336 + 6.25 = 12.378825336
x = 12.378825336

Simplifying
x = 12.378825336


Subproblem 2
x + -6.25 = -6.128825336

Simplifying
x + -6.25 = -6.128825336

Reorder the terms:
-6.25 + x = -6.128825336

Solving
-6.25 + x = -6.128825336

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -6.128825336 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -6.128825336 + 6.25
x = -6.128825336 + 6.25

Combine like terms: -6.128825336 + 6.25 = 0.121174664
x = 0.121174664

Simplifying
x = 0.121174664


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.378825336, 0.121174664}

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