0.1=15x+5.6x^2

Solution for 0.1=15x+5.6x^2 equation:

Simplifying
0.1 = 15x + 5.6x2

Solving
0.1 = 15x + 5.6x2

Solving for variable 'x'.

Reorder the terms:
0.1 + -15x + -5.6x2 = 15x + -15x + 5.6x2 + -5.6x2

Combine like terms: 15x + -15x = 0
0.1 + -15x + -5.6x2 = 0 + 5.6x2 + -5.6x2
0.1 + -15x + -5.6x2 = 5.6x2 + -5.6x2

Combine like terms: 5.6x2 + -5.6x2 = 0.0
0.1 + -15x + -5.6x2 = 0.0

Begin completing the square.  Divide all terms by
-5.6 the coefficient of the squared term: 

Divide each side by '-5.6'.
-0.01785714286 + 2.678571429x + x2 = 0

Move the constant term to the right:

Add '0.01785714286' to each side of the equation.
-0.01785714286 + 2.678571429x + 0.01785714286 + x2 = 0 + 0.01785714286

Reorder the terms:
-0.01785714286 + 0.01785714286 + 2.678571429x + x2 = 0 + 0.01785714286

Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000
0.00000000000 + 2.678571429x + x2 = 0 + 0.01785714286
2.678571429x + x2 = 0 + 0.01785714286

Combine like terms: 0 + 0.01785714286 = 0.01785714286
2.678571429x + x2 = 0.01785714286

The x term is 2.678571429x.  Take half its coefficient (1.339285715).
Square it (1.793686226) and add it to both sides.

Add '1.793686226' to each side of the equation.
2.678571429x + 1.793686226 + x2 = 0.01785714286 + 1.793686226

Reorder the terms:
1.793686226 + 2.678571429x + x2 = 0.01785714286 + 1.793686226

Combine like terms: 0.01785714286 + 1.793686226 = 1.81154336886
1.793686226 + 2.678571429x + x2 = 1.81154336886

Factor a perfect square on the left side:
(x + 1.339285715)(x + 1.339285715) = 1.81154336886

Calculate the square root of the right side: 1.345935871

Break this problem into two subproblems by setting 
(x + 1.339285715) equal to 1.345935871 and -1.345935871.

Subproblem 1
x + 1.339285715 = 1.345935871

Simplifying
x + 1.339285715 = 1.345935871

Reorder the terms:
1.339285715 + x = 1.345935871

Solving
1.339285715 + x = 1.345935871

Solving for variable 'x'.

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

Add '-1.339285715' to each side of the equation.
1.339285715 + -1.339285715 + x = 1.345935871 + -1.339285715

Combine like terms: 1.339285715 + -1.339285715 = 0.000000000
0.000000000 + x = 1.345935871 + -1.339285715
x = 1.345935871 + -1.339285715

Combine like terms: 1.345935871 + -1.339285715 = 0.006650156
x = 0.006650156

Simplifying
x = 0.006650156

Subproblem 2
x + 1.339285715 = -1.345935871

Simplifying
x + 1.339285715 = -1.345935871

Reorder the terms:
1.339285715 + x = -1.345935871

Solving
1.339285715 + x = -1.345935871

Solving for variable 'x'.

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

Add '-1.339285715' to each side of the equation.
1.339285715 + -1.339285715 + x = -1.345935871 + -1.339285715

Combine like terms: 1.339285715 + -1.339285715 = 0.000000000
0.000000000 + x = -1.345935871 + -1.339285715
x = -1.345935871 + -1.339285715

Combine like terms: -1.345935871 + -1.339285715 = -2.685221586
x = -2.685221586

Simplifying
x = -2.685221586

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.006650156, -2.685221586}