1.4x+(10.4-x)+x=x^2

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Solution for 1.4x+(10.4-x)+x=x^2 equation: 


Simplifying
1.4x + (10.4 + -1x) + x = x2

Remove parenthesis around (10.4 + -1x)
1.4x + 10.4 + -1x + x = x2

Reorder the terms:
10.4 + 1.4x + -1x + x = x2

Combine like terms: 1.4x + -1x = 0.4x
10.4 + 0.4x + x = x2

Combine like terms: 0.4x + x = 1.4x
10.4 + 1.4x = x2

Solving
10.4 + 1.4x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
10.4 + 1.4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10.4 + -1.4x + x2 = 0

Move the constant term to the right:

Add '10.4' to each side of the equation.
-10.4 + -1.4x + 10.4 + x2 = 0 + 10.4

Reorder the terms:
-10.4 + 10.4 + -1.4x + x2 = 0 + 10.4

Combine like terms: -10.4 + 10.4 = 0.0
0.0 + -1.4x + x2 = 0 + 10.4
-1.4x + x2 = 0 + 10.4

Combine like terms: 0 + 10.4 = 10.4
-1.4x + x2 = 10.4

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 10.4 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 10.4 + 0.49

Combine like terms: 10.4 + 0.49 = 10.89
0.49 + -1.4x + x2 = 10.89

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 10.89

Calculate the square root of the right side: 3.3

Break this problem into two subproblems by setting 
(x + -0.7) equal to 3.3 and -3.3.


Subproblem 1
x + -0.7 = 3.3

Simplifying
x + -0.7 = 3.3

Reorder the terms:
-0.7 + x = 3.3

Solving
-0.7 + x = 3.3

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 3.3 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 3.3 + 0.7
x = 3.3 + 0.7

Combine like terms: 3.3 + 0.7 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -0.7 = -3.3

Simplifying
x + -0.7 = -3.3

Reorder the terms:
-0.7 + x = -3.3

Solving
-0.7 + x = -3.3

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -3.3 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -3.3 + 0.7
x = -3.3 + 0.7

Combine like terms: -3.3 + 0.7 = -2.6
x = -2.6

Simplifying
x = -2.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -2.6}

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