x-12+x^2-4=3

Solution for x-12+x^2-4=3 equation:

Simplifying
x + -12 + x2 + -4 = 3

Reorder the terms:
-12 + -4 + x + x2 = 3

Combine like terms: -12 + -4 = -16
-16 + x + x2 = 3

Solving
-16 + x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-16 + -3 + x + x2 = 3 + -3

Combine like terms: -16 + -3 = -19
-19 + x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-19 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + x + x2 = 0 + 19
x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
x + x2 = 19

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 19 + 0.25

Reorder the terms:
0.25 + x + x2 = 19 + 0.25

Combine like terms: 19 + 0.25 = 19.25
0.25 + x + x2 = 19.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
x + 0.5 = 4.387482194

Simplifying
x + 0.5 = 4.387482194

Reorder the terms:
0.5 + x = 4.387482194

Solving
0.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.387482194 + -0.5
x = 4.387482194 + -0.5

Combine like terms: 4.387482194 + -0.5 = 3.887482194
x = 3.887482194

Simplifying
x = 3.887482194

Subproblem 2
x + 0.5 = -4.387482194

Simplifying
x + 0.5 = -4.387482194

Reorder the terms:
0.5 + x = -4.387482194

Solving
0.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.387482194 + -0.5
x = -4.387482194 + -0.5

Combine like terms: -4.387482194 + -0.5 = -4.887482194
x = -4.887482194

Simplifying
x = -4.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.887482194, -4.887482194}