(x-7)(x-7)=12

Solution for (x-7)(x-7)=12 equation:

Simplifying
(x + -7)(x + -7) = 12

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

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

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 12
((-7 * -7 + x * -7) + x(-7 + x)) = 12
((49 + -7x) + x(-7 + x)) = 12
(49 + -7x + (-7 * x + x * x)) = 12
(49 + -7x + (-7x + x2)) = 12

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 12

Solving
49 + -14x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
49 + -12 + -14x + x2 = 12 + -12

Combine like terms: 49 + -12 = 37
37 + -14x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
37 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + -14x + -37 + x2 = 0 + -37

Reorder the terms:
37 + -37 + -14x + x2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -14x + x2 = 0 + -37
-14x + x2 = 0 + -37

Combine like terms: 0 + -37 = -37
-14x + x2 = -37

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -37 + 49

Reorder the terms:
49 + -14x + x2 = -37 + 49

Combine like terms: -37 + 49 = 12
49 + -14x + x2 = 12

Factor a perfect square on the left side:
(x + -7)(x + -7) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -7) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -7 = 3.464101615

Simplifying
x + -7 = 3.464101615

Reorder the terms:
-7 + x = 3.464101615

Solving
-7 + x = 3.464101615

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 3.464101615 + 7

Combine like terms: -7 + 7 = 0
0 + x = 3.464101615 + 7
x = 3.464101615 + 7

Combine like terms: 3.464101615 + 7 = 10.464101615
x = 10.464101615

Simplifying
x = 10.464101615

Subproblem 2
x + -7 = -3.464101615

Simplifying
x + -7 = -3.464101615

Reorder the terms:
-7 + x = -3.464101615

Solving
-7 + x = -3.464101615

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -3.464101615 + 7

Combine like terms: -7 + 7 = 0
0 + x = -3.464101615 + 7
x = -3.464101615 + 7

Combine like terms: -3.464101615 + 7 = 3.535898385
x = 3.535898385

Simplifying
x = 3.535898385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.464101615, 3.535898385}