-0.5x^2+1.2x=0.4

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Solution for -0.5x^2+1.2x=0.4 equation: 


Simplifying
-0.5x2 + 1.2x = 0.4

Reorder the terms:
1.2x + -0.5x2 = 0.4

Solving
1.2x + -0.5x2 = 0.4

Solving for variable 'x'.

Reorder the terms:
-0.4 + 1.2x + -0.5x2 = 0.4 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
-0.4 + 1.2x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
0.8 + -2.4x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.4x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.4x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.4x + x2 = 0 + -0.8
-2.4x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.4x + x2 = -0.8

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = -0.8 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = -0.8 + 1.44

Combine like terms: -0.8 + 1.44 = 0.64
1.44 + -2.4x + x2 = 0.64

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 0.64

Calculate the square root of the right side: 0.8

Break this problem into two subproblems by setting 
(x + -1.2) equal to 0.8 and -0.8.


Subproblem 1
x + -1.2 = 0.8

Simplifying
x + -1.2 = 0.8

Reorder the terms:
-1.2 + x = 0.8

Solving
-1.2 + x = 0.8

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 0.8 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 0.8 + 1.2
x = 0.8 + 1.2

Combine like terms: 0.8 + 1.2 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + -1.2 = -0.8

Simplifying
x + -1.2 = -0.8

Reorder the terms:
-1.2 + x = -0.8

Solving
-1.2 + x = -0.8

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -0.8 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -0.8 + 1.2
x = -0.8 + 1.2

Combine like terms: -0.8 + 1.2 = 0.4
x = 0.4

Simplifying
x = 0.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, 0.4}

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