0.1=15x+0.56x^2

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Solution for 0.1=15x+0.56x^2 equation: 


Simplifying
0.1 = 15x + 0.56x2

Solving
0.1 = 15x + 0.56x2

Solving for variable 'x'.

Reorder the terms:
0.1 + -15x + -0.56x2 = 15x + -15x + 0.56x2 + -0.56x2

Combine like terms: 15x + -15x = 0
0.1 + -15x + -0.56x2 = 0 + 0.56x2 + -0.56x2
0.1 + -15x + -0.56x2 = 0.56x2 + -0.56x2

Combine like terms: 0.56x2 + -0.56x2 = 0.00
0.1 + -15x + -0.56x2 = 0.00

Begin completing the square.  Divide all terms by
-0.56 the coefficient of the squared term: 

Divide each side by '-0.56'.
-0.1785714286 + 26.78571429x + x2 = 0

Move the constant term to the right:

Add '0.1785714286' to each side of the equation.
-0.1785714286 + 26.78571429x + 0.1785714286 + x2 = 0 + 0.1785714286

Reorder the terms:
-0.1785714286 + 0.1785714286 + 26.78571429x + x2 = 0 + 0.1785714286

Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000
0.0000000000 + 26.78571429x + x2 = 0 + 0.1785714286
26.78571429x + x2 = 0 + 0.1785714286

Combine like terms: 0 + 0.1785714286 = 0.1785714286
26.78571429x + x2 = 0.1785714286

The x term is 26.78571429x.  Take half its coefficient (13.39285715).
Square it (179.3686226) and add it to both sides.

Add '179.3686226' to each side of the equation.
26.78571429x + 179.3686226 + x2 = 0.1785714286 + 179.3686226

Reorder the terms:
179.3686226 + 26.78571429x + x2 = 0.1785714286 + 179.3686226

Combine like terms: 0.1785714286 + 179.3686226 = 179.5471940286
179.3686226 + 26.78571429x + x2 = 179.5471940286

Factor a perfect square on the left side:
(x + 13.39285715)(x + 13.39285715) = 179.5471940286

Calculate the square root of the right side: 13.399522157

Break this problem into two subproblems by setting 
(x + 13.39285715) equal to 13.399522157 and -13.399522157.


Subproblem 1
x + 13.39285715 = 13.399522157

Simplifying
x + 13.39285715 = 13.399522157

Reorder the terms:
13.39285715 + x = 13.399522157

Solving
13.39285715 + x = 13.399522157

Solving for variable 'x'.

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

Add '-13.39285715' to each side of the equation.
13.39285715 + -13.39285715 + x = 13.399522157 + -13.39285715

Combine like terms: 13.39285715 + -13.39285715 = 0.00000000
0.00000000 + x = 13.399522157 + -13.39285715
x = 13.399522157 + -13.39285715

Combine like terms: 13.399522157 + -13.39285715 = 0.006665007
x = 0.006665007

Simplifying
x = 0.006665007


Subproblem 2
x + 13.39285715 = -13.399522157

Simplifying
x + 13.39285715 = -13.399522157

Reorder the terms:
13.39285715 + x = -13.399522157

Solving
13.39285715 + x = -13.399522157

Solving for variable 'x'.

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

Add '-13.39285715' to each side of the equation.
13.39285715 + -13.39285715 + x = -13.399522157 + -13.39285715

Combine like terms: 13.39285715 + -13.39285715 = 0.00000000
0.00000000 + x = -13.399522157 + -13.39285715
x = -13.399522157 + -13.39285715

Combine like terms: -13.399522157 + -13.39285715 = -26.792379307
x = -26.792379307

Simplifying
x = -26.792379307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.006665007, -26.792379307}

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