(x^2)+(12x)+(36)=7

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Solution for (x^2)+(12x)+(36)=7 equation: 


Simplifying
(x2) + (12x) + (36) = 7
x2 + (12x) + (36) = 7
x2 + (12x) + 36 = 7

Reorder the terms:
36 + (12x) + x2 = 7

Solving
36 + (12x) + x2 = 7

Solving for variable 'x'.

Reorder the terms:
36 + -7 + (12x) + x2 = 7 + -7

Combine like terms: 36 + -7 = 29
29 + (12x) + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
29 + (12x) + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + (12x) + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + (12x) + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + (12x) + x2 = 0 + -29
(12x) + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
(12x) + x2 = -29

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 = -29 + 36

Reorder the terms:
36 + (12x) + x2 = -29 + 36

Combine like terms: -29 + 36 = 7
36 + (12x) + x2 = 7

Factor a perfect square on the left side:
(x + 6)(x + 6) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 6) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 6 = 2.645751311

Simplifying
x + 6 = 2.645751311

Reorder the terms:
6 + x = 2.645751311

Solving
6 + x = 2.645751311

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 = 2.645751311 + -6

Combine like terms: 6 + -6 = 0
0 + x = 2.645751311 + -6
x = 2.645751311 + -6

Combine like terms: 2.645751311 + -6 = -3.354248689
x = -3.354248689

Simplifying
x = -3.354248689


Subproblem 2
x + 6 = -2.645751311

Simplifying
x + 6 = -2.645751311

Reorder the terms:
6 + x = -2.645751311

Solving
6 + x = -2.645751311

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 = -2.645751311 + -6

Combine like terms: 6 + -6 = 0
0 + x = -2.645751311 + -6
x = -2.645751311 + -6

Combine like terms: -2.645751311 + -6 = -8.645751311
x = -8.645751311

Simplifying
x = -8.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.354248689, -8.645751311}

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