.4x+x^2=1.2

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Solution for .4x+x^2=1.2 equation: 


Simplifying
0.4x + x2 = 1.2

Solving
0.4x + x2 = 1.2

Solving for variable 'x'.

Reorder the terms:
-1.2 + 0.4x + x2 = 1.2 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + 0.4x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.4x + 1.2 + x2 = 0.0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.4x + x2 = 0.0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.4x + x2 = 0.0 + 1.2
0.4x + x2 = 0.0 + 1.2

Combine like terms: 0.0 + 1.2 = 1.2
0.4x + x2 = 1.2

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 1.2 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 1.2 + 0.04

Combine like terms: 1.2 + 0.04 = 1.24
0.04 + 0.4x + x2 = 1.24

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1.113552873 and -1.113552873.


Subproblem 1
x + 0.2 = 1.113552873

Simplifying
x + 0.2 = 1.113552873

Reorder the terms:
0.2 + x = 1.113552873

Solving
0.2 + x = 1.113552873

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 1.113552873 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 1.113552873 + -0.2
x = 1.113552873 + -0.2

Combine like terms: 1.113552873 + -0.2 = 0.913552873
x = 0.913552873

Simplifying
x = 0.913552873


Subproblem 2
x + 0.2 = -1.113552873

Simplifying
x + 0.2 = -1.113552873

Reorder the terms:
0.2 + x = -1.113552873

Solving
0.2 + x = -1.113552873

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -1.113552873 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -1.113552873 + -0.2
x = -1.113552873 + -0.2

Combine like terms: -1.113552873 + -0.2 = -1.313552873
x = -1.313552873

Simplifying
x = -1.313552873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.913552873, -1.313552873}

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