x^2-3.6x+2.4=0

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Solution for x^2-3.6x+2.4=0 equation: 


Simplifying
x2 + -3.6x + 2.4 = 0

Reorder the terms:
2.4 + -3.6x + x2 = 0

Solving
2.4 + -3.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -3.6x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -3.6x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -3.6x + x2 = 0 + -2.4
-3.6x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-3.6x + x2 = -2.4

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = -2.4 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = -2.4 + 3.24

Combine like terms: -2.4 + 3.24 = 0.84
3.24 + -3.6x + x2 = 0.84

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(x + -1.8) equal to 0.916515139 and -0.916515139.


Subproblem 1
x + -1.8 = 0.916515139

Simplifying
x + -1.8 = 0.916515139

Reorder the terms:
-1.8 + x = 0.916515139

Solving
-1.8 + x = 0.916515139

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = 0.916515139 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = 0.916515139 + 1.8
x = 0.916515139 + 1.8

Combine like terms: 0.916515139 + 1.8 = 2.716515139
x = 2.716515139

Simplifying
x = 2.716515139


Subproblem 2
x + -1.8 = -0.916515139

Simplifying
x + -1.8 = -0.916515139

Reorder the terms:
-1.8 + x = -0.916515139

Solving
-1.8 + x = -0.916515139

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = -0.916515139 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = -0.916515139 + 1.8
x = -0.916515139 + 1.8

Combine like terms: -0.916515139 + 1.8 = 0.883484861
x = 0.883484861

Simplifying
x = 0.883484861


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.716515139, 0.883484861}

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