x^2+45x+2x+2=3

Solution for x^2+45x+2x+2=3 equation:

Simplifying
x2 + 45x + 2x + 2 = 3

Reorder the terms:
2 + 45x + 2x + x2 = 3

Combine like terms: 45x + 2x = 47x
2 + 47x + x2 = 3

Solving
2 + 47x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
2 + -3 + 47x + x2 = 3 + -3

Combine like terms: 2 + -3 = -1
-1 + 47x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-1 + 47x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 47x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 47x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 47x + x2 = 0 + 1
47x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
47x + x2 = 1

The x term is 47x.  Take half its coefficient (23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
47x + 552.25 + x2 = 1 + 552.25

Reorder the terms:
552.25 + 47x + x2 = 1 + 552.25

Combine like terms: 1 + 552.25 = 553.25
552.25 + 47x + x2 = 553.25

Factor a perfect square on the left side:
(x + 23.5)(x + 23.5) = 553.25

Calculate the square root of the right side: 23.521266973

Break this problem into two subproblems by setting 
(x + 23.5) equal to 23.521266973 and -23.521266973.

Subproblem 1
x + 23.5 = 23.521266973

Simplifying
x + 23.5 = 23.521266973

Reorder the terms:
23.5 + x = 23.521266973

Solving
23.5 + x = 23.521266973

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = 23.521266973 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = 23.521266973 + -23.5
x = 23.521266973 + -23.5

Combine like terms: 23.521266973 + -23.5 = 0.021266973
x = 0.021266973

Simplifying
x = 0.021266973

Subproblem 2
x + 23.5 = -23.521266973

Simplifying
x + 23.5 = -23.521266973

Reorder the terms:
23.5 + x = -23.521266973

Solving
23.5 + x = -23.521266973

Solving for variable 'x'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + x = -23.521266973 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + x = -23.521266973 + -23.5
x = -23.521266973 + -23.5

Combine like terms: -23.521266973 + -23.5 = -47.021266973
x = -47.021266973

Simplifying
x = -47.021266973

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.021266973, -47.021266973}