x^2+0.12x-0.8=0

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Solution for x^2+0.12x-0.8=0 equation: 


Simplifying
x2 + 0.12x + -0.8 = 0

Reorder the terms:
-0.8 + 0.12x + x2 = 0

Solving
-0.8 + 0.12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 0.12x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 0.12x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 0.12x + x2 = 0 + 0.8
0.12x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
0.12x + x2 = 0.8

The x term is 0.12x.  Take half its coefficient (0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
0.12x + 0.0036 + x2 = 0.8 + 0.0036

Reorder the terms:
0.0036 + 0.12x + x2 = 0.8 + 0.0036

Combine like terms: 0.8 + 0.0036 = 0.8036
0.0036 + 0.12x + x2 = 0.8036

Factor a perfect square on the left side:
(x + 0.06)(x + 0.06) = 0.8036

Calculate the square root of the right side: 0.896437393

Break this problem into two subproblems by setting 
(x + 0.06) equal to 0.896437393 and -0.896437393.


Subproblem 1
x + 0.06 = 0.896437393

Simplifying
x + 0.06 = 0.896437393

Reorder the terms:
0.06 + x = 0.896437393

Solving
0.06 + x = 0.896437393

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = 0.896437393 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = 0.896437393 + -0.06
x = 0.896437393 + -0.06

Combine like terms: 0.896437393 + -0.06 = 0.836437393
x = 0.836437393

Simplifying
x = 0.836437393


Subproblem 2
x + 0.06 = -0.896437393

Simplifying
x + 0.06 = -0.896437393

Reorder the terms:
0.06 + x = -0.896437393

Solving
0.06 + x = -0.896437393

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = -0.896437393 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = -0.896437393 + -0.06
x = -0.896437393 + -0.06

Combine like terms: -0.896437393 + -0.06 = -0.956437393
x = -0.956437393

Simplifying
x = -0.956437393


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.836437393, -0.956437393}

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