.1242=x^2+1.80x

Solution for .1242=x^2+1.80x equation:

Simplifying
0.1242 = x2 + 1.80x

Reorder the terms:
0.1242 = 1.80x + x2

Solving
0.1242 = 1.80x + x2

Solving for variable 'x'.

Reorder the terms:
0.1242 + -1.80x + -1x2 = 1.80x + -1.80x + x2 + -1x2

Combine like terms: 1.80x + -1.80x = 0.00
0.1242 + -1.80x + -1x2 = 0.00 + x2 + -1x2
0.1242 + -1.80x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.1242 + -1.80x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.1242 + 1.8x + x2 = 0

Move the constant term to the right:

Add '0.1242' to each side of the equation.
-0.1242 + 1.8x + 0.1242 + x2 = 0 + 0.1242

Reorder the terms:
-0.1242 + 0.1242 + 1.8x + x2 = 0 + 0.1242

Combine like terms: -0.1242 + 0.1242 = 0.0000
0.0000 + 1.8x + x2 = 0 + 0.1242
1.8x + x2 = 0 + 0.1242

Combine like terms: 0 + 0.1242 = 0.1242
1.8x + x2 = 0.1242

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 0.1242 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.1242 + 0.81

Combine like terms: 0.1242 + 0.81 = 0.9342
0.81 + 1.8x + x2 = 0.9342

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 0.9342

Calculate the square root of the right side: 0.966540222

Break this problem into two subproblems by setting 
(x + 0.9) equal to 0.966540222 and -0.966540222.

Subproblem 1
x + 0.9 = 0.966540222

Simplifying
x + 0.9 = 0.966540222

Reorder the terms:
0.9 + x = 0.966540222

Solving
0.9 + x = 0.966540222

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 0.966540222 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 0.966540222 + -0.9
x = 0.966540222 + -0.9

Combine like terms: 0.966540222 + -0.9 = 0.066540222
x = 0.066540222

Simplifying
x = 0.066540222

Subproblem 2
x + 0.9 = -0.966540222

Simplifying
x + 0.9 = -0.966540222

Reorder the terms:
0.9 + x = -0.966540222

Solving
0.9 + x = -0.966540222

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -0.966540222 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -0.966540222 + -0.9
x = -0.966540222 + -0.9

Combine like terms: -0.966540222 + -0.9 = -1.866540222
x = -1.866540222

Simplifying
x = -1.866540222

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.066540222, -1.866540222}