12x+6+x^2+47=90

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Solution for 12x+6+x^2+47=90 equation: 


Simplifying
12x + 6 + x2 + 47 = 90

Reorder the terms:
6 + 47 + 12x + x2 = 90

Combine like terms: 6 + 47 = 53
53 + 12x + x2 = 90

Solving
53 + 12x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
53 + -90 + 12x + x2 = 90 + -90

Combine like terms: 53 + -90 = -37
-37 + 12x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-37 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 12x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 12x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 12x + x2 = 0 + 37
12x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
12x + x2 = 37

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 37 + 36

Reorder the terms:
36 + 12x + x2 = 37 + 36

Combine like terms: 37 + 36 = 73
36 + 12x + x2 = 73

Factor a perfect square on the left side:
(x + 6)(x + 6) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 6) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + 6 = 8.544003745

Simplifying
x + 6 = 8.544003745

Reorder the terms:
6 + x = 8.544003745

Solving
6 + x = 8.544003745

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 8.544003745 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8.544003745 + -6
x = 8.544003745 + -6

Combine like terms: 8.544003745 + -6 = 2.544003745
x = 2.544003745

Simplifying
x = 2.544003745


Subproblem 2
x + 6 = -8.544003745

Simplifying
x + 6 = -8.544003745

Reorder the terms:
6 + x = -8.544003745

Solving
6 + x = -8.544003745

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -8.544003745 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8.544003745 + -6
x = -8.544003745 + -6

Combine like terms: -8.544003745 + -6 = -14.544003745
x = -14.544003745

Simplifying
x = -14.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.544003745, -14.544003745}

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