-0.4x^2+3x-4.5=0

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Solution for -0.4x^2+3x-4.5=0 equation: 


Simplifying
-0.4x2 + 3x + -4.5 = 0

Reorder the terms:
-4.5 + 3x + -0.4x2 = 0

Solving
-4.5 + 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'.
11.25 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + -7.5x + -11.25 + x2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + -7.5x + x2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + -7.5x + x2 = 0 + -11.25
-7.5x + x2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
-7.5x + x2 = -11.25

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 = -11.25 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -11.25 + 14.0625

Combine like terms: -11.25 + 14.0625 = 2.8125
14.0625 + -7.5x + x2 = 2.8125

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 2.8125

Calculate the square root of the right side: 1.677050983

Break this problem into two subproblems by setting 
(x + -3.75) equal to 1.677050983 and -1.677050983.


Subproblem 1
x + -3.75 = 1.677050983

Simplifying
x + -3.75 = 1.677050983

Reorder the terms:
-3.75 + x = 1.677050983

Solving
-3.75 + x = 1.677050983

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 = 1.677050983 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 1.677050983 + 3.75
x = 1.677050983 + 3.75

Combine like terms: 1.677050983 + 3.75 = 5.427050983
x = 5.427050983

Simplifying
x = 5.427050983


Subproblem 2
x + -3.75 = -1.677050983

Simplifying
x + -3.75 = -1.677050983

Reorder the terms:
-3.75 + x = -1.677050983

Solving
-3.75 + x = -1.677050983

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 = -1.677050983 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -1.677050983 + 3.75
x = -1.677050983 + 3.75

Combine like terms: -1.677050983 + 3.75 = 2.072949017
x = 2.072949017

Simplifying
x = 2.072949017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.427050983, 2.072949017}

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