(x+1.5)(x+1.5)+13=141

Solution for (x+1.5)(x+1.5)+13=141 equation:

Simplifying
(x + 1.5)(x + 1.5) + 13 = 141

Reorder the terms:
(1.5 + x)(x + 1.5) + 13 = 141

Reorder the terms:
(1.5 + x)(1.5 + x) + 13 = 141

Multiply (1.5 + x) * (1.5 + x)
(1.5(1.5 + x) + x(1.5 + x)) + 13 = 141
((1.5 * 1.5 + x * 1.5) + x(1.5 + x)) + 13 = 141
((2.25 + 1.5x) + x(1.5 + x)) + 13 = 141
(2.25 + 1.5x + (1.5 * x + x * x)) + 13 = 141
(2.25 + 1.5x + (1.5x + x2)) + 13 = 141

Combine like terms: 1.5x + 1.5x = 3x
(2.25 + 3x + x2) + 13 = 141

Reorder the terms:
2.25 + 13 + 3x + x2 = 141

Combine like terms: 2.25 + 13 = 15.25
15.25 + 3x + x2 = 141

Solving
15.25 + 3x + x2 = 141

Solving for variable 'x'.

Reorder the terms:
15.25 + -141 + 3x + x2 = 141 + -141

Combine like terms: 15.25 + -141 = -125.75
-125.75 + 3x + x2 = 141 + -141

Combine like terms: 141 + -141 = 0
-125.75 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125.75' to each side of the equation.
-125.75 + 3x + 125.75 + x2 = 0 + 125.75

Reorder the terms:
-125.75 + 125.75 + 3x + x2 = 0 + 125.75

Combine like terms: -125.75 + 125.75 = 0.00
0.00 + 3x + x2 = 0 + 125.75
3x + x2 = 0 + 125.75

Combine like terms: 0 + 125.75 = 125.75
3x + x2 = 125.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 125.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 125.75 + 2.25

Combine like terms: 125.75 + 2.25 = 128
2.25 + 3x + x2 = 128

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11.313708499 and -11.313708499.

Subproblem 1
x + 1.5 = 11.313708499

Simplifying
x + 1.5 = 11.313708499

Reorder the terms:
1.5 + x = 11.313708499

Solving
1.5 + x = 11.313708499

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 11.313708499 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 11.313708499 + -1.5
x = 11.313708499 + -1.5

Combine like terms: 11.313708499 + -1.5 = 9.813708499
x = 9.813708499

Simplifying
x = 9.813708499

Subproblem 2
x + 1.5 = -11.313708499

Simplifying
x + 1.5 = -11.313708499

Reorder the terms:
1.5 + x = -11.313708499

Solving
1.5 + x = -11.313708499

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -11.313708499 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -11.313708499 + -1.5
x = -11.313708499 + -1.5

Combine like terms: -11.313708499 + -1.5 = -12.813708499
x = -12.813708499

Simplifying
x = -12.813708499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.813708499, -12.813708499}