.15x^2-14x+.125=0

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Solution for .15x^2-14x+.125=0 equation: 


Simplifying
0.15x2 + -14x + 0.125 = 0

Reorder the terms:
0.125 + -14x + 0.15x2 = 0

Solving
0.125 + -14x + 0.15x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.15'.
0.8333333333 + -93.33333333x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -93.33333333x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -93.33333333x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -93.33333333x + x2 = 0 + -0.8333333333
-93.33333333x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-93.33333333x + x2 = -0.8333333333

The x term is -93.33333333x.  Take half its coefficient (-46.66666667).
Square it (2177.777778) and add it to both sides.

Add '2177.777778' to each side of the equation.
-93.33333333x + 2177.777778 + x2 = -0.8333333333 + 2177.777778

Reorder the terms:
2177.777778 + -93.33333333x + x2 = -0.8333333333 + 2177.777778

Combine like terms: -0.8333333333 + 2177.777778 = 2176.9444446667
2177.777778 + -93.33333333x + x2 = 2176.9444446667

Factor a perfect square on the left side:
(x + -46.66666667)(x + -46.66666667) = 2176.9444446667

Calculate the square root of the right side: 46.657737243

Break this problem into two subproblems by setting 
(x + -46.66666667) equal to 46.657737243 and -46.657737243.


Subproblem 1
x + -46.66666667 = 46.657737243

Simplifying
x + -46.66666667 = 46.657737243

Reorder the terms:
-46.66666667 + x = 46.657737243

Solving
-46.66666667 + x = 46.657737243

Solving for variable 'x'.

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

Add '46.66666667' to each side of the equation.
-46.66666667 + 46.66666667 + x = 46.657737243 + 46.66666667

Combine like terms: -46.66666667 + 46.66666667 = 0.00000000
0.00000000 + x = 46.657737243 + 46.66666667
x = 46.657737243 + 46.66666667

Combine like terms: 46.657737243 + 46.66666667 = 93.324403913
x = 93.324403913

Simplifying
x = 93.324403913


Subproblem 2
x + -46.66666667 = -46.657737243

Simplifying
x + -46.66666667 = -46.657737243

Reorder the terms:
-46.66666667 + x = -46.657737243

Solving
-46.66666667 + x = -46.657737243

Solving for variable 'x'.

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

Add '46.66666667' to each side of the equation.
-46.66666667 + 46.66666667 + x = -46.657737243 + 46.66666667

Combine like terms: -46.66666667 + 46.66666667 = 0.00000000
0.00000000 + x = -46.657737243 + 46.66666667
x = -46.657737243 + 46.66666667

Combine like terms: -46.657737243 + 46.66666667 = 0.008929427
x = 0.008929427

Simplifying
x = 0.008929427


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {93.324403913, 0.008929427}

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