x+144=(x+7)(x+7)

Solution for x+144=(x+7)(x+7) equation:

Simplifying
x + 144 = (x + 7)(x + 7)

Reorder the terms:
144 + x = (x + 7)(x + 7)

Reorder the terms:
144 + x = (7 + x)(x + 7)

Reorder the terms:
144 + x = (7 + x)(7 + x)

Multiply (7 + x) * (7 + x)
144 + x = (7(7 + x) + x(7 + x))
144 + x = ((7 * 7 + x * 7) + x(7 + x))
144 + x = ((49 + 7x) + x(7 + x))
144 + x = (49 + 7x + (7 * x + x * x))
144 + x = (49 + 7x + (7x + x2))

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

Solving
144 + x = 49 + 14x + x2

Solving for variable 'x'.

Reorder the terms:
144 + -49 + x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Combine like terms: 144 + -49 = 95
95 + x + -14x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Combine like terms: x + -14x = -13x
95 + -13x + -1x2 = 49 + 14x + x2 + -49 + -14x + -1x2

Reorder the terms:
95 + -13x + -1x2 = 49 + -49 + 14x + -14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
95 + -13x + -1x2 = 0 + 14x + -14x + x2 + -1x2
95 + -13x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
95 + -13x + -1x2 = 0 + x2 + -1x2
95 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
95 + -13x + -1x2 = 0

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

Divide each side by '-1'.
-95 + 13x + x2 = 0

Move the constant term to the right:

Add '95' to each side of the equation.
-95 + 13x + 95 + x2 = 0 + 95

Reorder the terms:
-95 + 95 + 13x + x2 = 0 + 95

Combine like terms: -95 + 95 = 0
0 + 13x + x2 = 0 + 95
13x + x2 = 0 + 95

Combine like terms: 0 + 95 = 95
13x + x2 = 95

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 95 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 95 + 42.25

Combine like terms: 95 + 42.25 = 137.25
42.25 + 13x + x2 = 137.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 137.25

Calculate the square root of the right side: 11.715374514

Break this problem into two subproblems by setting 
(x + 6.5) equal to 11.715374514 and -11.715374514.

Subproblem 1
x + 6.5 = 11.715374514

Simplifying
x + 6.5 = 11.715374514

Reorder the terms:
6.5 + x = 11.715374514

Solving
6.5 + x = 11.715374514

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 11.715374514 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 11.715374514 + -6.5
x = 11.715374514 + -6.5

Combine like terms: 11.715374514 + -6.5 = 5.215374514
x = 5.215374514

Simplifying
x = 5.215374514

Subproblem 2
x + 6.5 = -11.715374514

Simplifying
x + 6.5 = -11.715374514

Reorder the terms:
6.5 + x = -11.715374514

Solving
6.5 + x = -11.715374514

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -11.715374514 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -11.715374514 + -6.5
x = -11.715374514 + -6.5

Combine like terms: -11.715374514 + -6.5 = -18.215374514
x = -18.215374514

Simplifying
x = -18.215374514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.215374514, -18.215374514}