x^2-7.2x+12.8=0

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Solution for x^2-7.2x+12.8=0 equation: 


Simplifying
x2 + -7.2x + 12.8 = 0

Reorder the terms:
12.8 + -7.2x + x2 = 0

Solving
12.8 + -7.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12.8' to each side of the equation.
12.8 + -7.2x + -12.8 + x2 = 0 + -12.8

Reorder the terms:
12.8 + -12.8 + -7.2x + x2 = 0 + -12.8

Combine like terms: 12.8 + -12.8 = 0.0
0.0 + -7.2x + x2 = 0 + -12.8
-7.2x + x2 = 0 + -12.8

Combine like terms: 0 + -12.8 = -12.8
-7.2x + x2 = -12.8

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = -12.8 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = -12.8 + 12.96

Combine like terms: -12.8 + 12.96 = 0.16
12.96 + -7.2x + x2 = 0.16

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + -3.6) equal to 0.4 and -0.4.


Subproblem 1
x + -3.6 = 0.4

Simplifying
x + -3.6 = 0.4

Reorder the terms:
-3.6 + x = 0.4

Solving
-3.6 + x = 0.4

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = 0.4 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = 0.4 + 3.6
x = 0.4 + 3.6

Combine like terms: 0.4 + 3.6 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -3.6 = -0.4

Simplifying
x + -3.6 = -0.4

Reorder the terms:
-3.6 + x = -0.4

Solving
-3.6 + x = -0.4

Solving for variable 'x'.

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

Add '3.6' to each side of the equation.
-3.6 + 3.6 + x = -0.4 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + x = -0.4 + 3.6
x = -0.4 + 3.6

Combine like terms: -0.4 + 3.6 = 3.2
x = 3.2

Simplifying
x = 3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, 3.2}

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