0.5x^2+0.4x-1.2=0

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Solution for 0.5x^2+0.4x-1.2=0 equation: 


Simplifying
0.5x2 + 0.4x + -1.2 = 0

Reorder the terms:
-1.2 + 0.4x + 0.5x2 = 0

Solving
-1.2 + 0.4x + 0.5x2 = 0

Solving for variable 'x'.

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

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

Move the constant term to the right:

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

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

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

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

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 2.4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 2.4 + 0.16

Combine like terms: 2.4 + 0.16 = 2.56
0.16 + 0.8x + x2 = 2.56

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 2.56

Calculate the square root of the right side: 1.6

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.6 and -1.6.


Subproblem 1
x + 0.4 = 1.6

Simplifying
x + 0.4 = 1.6

Reorder the terms:
0.4 + x = 1.6

Solving
0.4 + x = 1.6

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.6 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.6 + -0.4
x = 1.6 + -0.4

Combine like terms: 1.6 + -0.4 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + 0.4 = -1.6

Simplifying
x + 0.4 = -1.6

Reorder the terms:
0.4 + x = -1.6

Solving
0.4 + x = -1.6

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.6 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.6 + -0.4
x = -1.6 + -0.4

Combine like terms: -1.6 + -0.4 = -2
x = -2

Simplifying
x = -2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, -2}

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