x^2+4x+4=22026.46579

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Solution for x^2+4x+4=22026.46579 equation: 


Simplifying
x2 + 4x + 4 = 22026.46579

Reorder the terms:
4 + 4x + x2 = 22026.46579

Solving
4 + 4x + x2 = 22026.46579

Solving for variable 'x'.

Reorder the terms:
4 + -22026.46579 + 4x + x2 = 22026.46579 + -22026.46579

Combine like terms: 4 + -22026.46579 = -22022.46579
-22022.46579 + 4x + x2 = 22026.46579 + -22026.46579

Combine like terms: 22026.46579 + -22026.46579 = 0.00000
-22022.46579 + 4x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '22022.46579' to each side of the equation.
-22022.46579 + 4x + 22022.46579 + x2 = 0.00000 + 22022.46579

Reorder the terms:
-22022.46579 + 22022.46579 + 4x + x2 = 0.00000 + 22022.46579

Combine like terms: -22022.46579 + 22022.46579 = 0.00000
0.00000 + 4x + x2 = 0.00000 + 22022.46579
4x + x2 = 0.00000 + 22022.46579

Combine like terms: 0.00000 + 22022.46579 = 22022.46579
4x + x2 = 22022.46579

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 22022.46579 + 4

Reorder the terms:
4 + 4x + x2 = 22022.46579 + 4

Combine like terms: 22022.46579 + 4 = 22026.46579
4 + 4x + x2 = 22026.46579

Factor a perfect square on the left side:
(x + 2)(x + 2) = 22026.46579

Calculate the square root of the right side: 148.413159086

Break this problem into two subproblems by setting 
(x + 2) equal to 148.413159086 and -148.413159086.


Subproblem 1
x + 2 = 148.413159086

Simplifying
x + 2 = 148.413159086

Reorder the terms:
2 + x = 148.413159086

Solving
2 + x = 148.413159086

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 148.413159086 + -2

Combine like terms: 2 + -2 = 0
0 + x = 148.413159086 + -2
x = 148.413159086 + -2

Combine like terms: 148.413159086 + -2 = 146.413159086
x = 146.413159086

Simplifying
x = 146.413159086


Subproblem 2
x + 2 = -148.413159086

Simplifying
x + 2 = -148.413159086

Reorder the terms:
2 + x = -148.413159086

Solving
2 + x = -148.413159086

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -148.413159086 + -2

Combine like terms: 2 + -2 = 0
0 + x = -148.413159086 + -2
x = -148.413159086 + -2

Combine like terms: -148.413159086 + -2 = -150.413159086
x = -150.413159086

Simplifying
x = -150.413159086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {146.413159086, -150.413159086}

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