13x^2+5x-8=36+12x+x^2

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Solution for 13x^2+5x-8=36+12x+x^2 equation: 


Simplifying
13x2 + 5x + -8 = 36 + 12x + x2

Reorder the terms:
-8 + 5x + 13x2 = 36 + 12x + x2

Solving
-8 + 5x + 13x2 = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
-8 + -36 + 5x + -12x + 13x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: -8 + -36 = -44
-44 + 5x + -12x + 13x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 5x + -12x = -7x
-44 + -7x + 13x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 13x2 + -1x2 = 12x2
-44 + -7x + 12x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
-44 + -7x + 12x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-44 + -7x + 12x2 = 0 + 12x + -12x + x2 + -1x2
-44 + -7x + 12x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-44 + -7x + 12x2 = 0 + x2 + -1x2
-44 + -7x + 12x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-44 + -7x + 12x2 = 0

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

Divide each side by '12'.
-3.666666667 + -0.5833333333x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -0.5833333333x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -0.5833333333x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -0.5833333333x + x2 = 0 + 3.666666667
-0.5833333333x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-0.5833333333x + x2 = 3.666666667

The x term is -0.5833333333x.  Take half its coefficient (-0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
-0.5833333333x + 0.08506944446 + x2 = 3.666666667 + 0.08506944446

Reorder the terms:
0.08506944446 + -0.5833333333x + x2 = 3.666666667 + 0.08506944446

Combine like terms: 3.666666667 + 0.08506944446 = 3.75173611146
0.08506944446 + -0.5833333333x + x2 = 3.75173611146

Factor a perfect square on the left side:
(x + -0.2916666667)(x + -0.2916666667) = 3.75173611146

Calculate the square root of the right side: 1.936939883

Break this problem into two subproblems by setting 
(x + -0.2916666667) equal to 1.936939883 and -1.936939883.


Subproblem 1
x + -0.2916666667 = 1.936939883

Simplifying
x + -0.2916666667 = 1.936939883

Reorder the terms:
-0.2916666667 + x = 1.936939883

Solving
-0.2916666667 + x = 1.936939883

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = 1.936939883 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = 1.936939883 + 0.2916666667
x = 1.936939883 + 0.2916666667

Combine like terms: 1.936939883 + 0.2916666667 = 2.2286065497
x = 2.2286065497

Simplifying
x = 2.2286065497


Subproblem 2
x + -0.2916666667 = -1.936939883

Simplifying
x + -0.2916666667 = -1.936939883

Reorder the terms:
-0.2916666667 + x = -1.936939883

Solving
-0.2916666667 + x = -1.936939883

Solving for variable 'x'.

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

Add '0.2916666667' to each side of the equation.
-0.2916666667 + 0.2916666667 + x = -1.936939883 + 0.2916666667

Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000
0.0000000000 + x = -1.936939883 + 0.2916666667
x = -1.936939883 + 0.2916666667

Combine like terms: -1.936939883 + 0.2916666667 = -1.6452732163
x = -1.6452732163

Simplifying
x = -1.6452732163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2286065497, -1.6452732163}

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