-0.4x^2+3x+0.5=0

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Solution for -0.4x^2+3x+0.5=0 equation: 


Simplifying
-0.4x2 + 3x + 0.5 = 0

Reorder the terms:
0.5 + 3x + -0.4x2 = 0

Solving
0.5 + 3x + -0.4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.4 the coefficient of the squared term: 

Divide each side by '-0.4'.
-1.25 + -7.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -7.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -7.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -7.5x + x2 = 0 + 1.25
-7.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-7.5x + x2 = 1.25

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 1.25 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 1.25 + 14.0625

Combine like terms: 1.25 + 14.0625 = 15.3125
14.0625 + -7.5x + x2 = 15.3125

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 15.3125

Calculate the square root of the right side: 3.913118961

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.913118961 and -3.913118961.


Subproblem 1
x + -3.75 = 3.913118961

Simplifying
x + -3.75 = 3.913118961

Reorder the terms:
-3.75 + x = 3.913118961

Solving
-3.75 + x = 3.913118961

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.913118961 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.913118961 + 3.75
x = 3.913118961 + 3.75

Combine like terms: 3.913118961 + 3.75 = 7.663118961
x = 7.663118961

Simplifying
x = 7.663118961


Subproblem 2
x + -3.75 = -3.913118961

Simplifying
x + -3.75 = -3.913118961

Reorder the terms:
-3.75 + x = -3.913118961

Solving
-3.75 + x = -3.913118961

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.913118961 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.913118961 + 3.75
x = -3.913118961 + 3.75

Combine like terms: -3.913118961 + 3.75 = -0.163118961
x = -0.163118961

Simplifying
x = -0.163118961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.663118961, -0.163118961}

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