0=x^2+6x+4

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Solution for 0=x^2+6x+4 equation: 


Simplifying
0 = x2 + 6x + 4

Reorder the terms:
0 = 4 + 6x + x2

Solving
0 = 4 + 6x + x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -6x + -1x2 = 4 + 6x + x2 + -4 + -6x + -1x2

Reorder the terms:
-4 + -6x + -1x2 = 4 + -4 + 6x + -6x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-4 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-4 + -6x + -1x2 = 0 + x2 + -1x2
-4 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 6x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 6x + x2 = 0

Solving
4 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6x + x2 = 0 + -4
6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
6x + x2 = -4

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -4 + 9

Reorder the terms:
9 + 6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + 6x + x2 = 5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 3) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + 3 = 2.236067978

Simplifying
x + 3 = 2.236067978

Reorder the terms:
3 + x = 2.236067978

Solving
3 + x = 2.236067978

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.236067978 + -3
x = 2.236067978 + -3

Combine like terms: 2.236067978 + -3 = -0.763932022
x = -0.763932022

Simplifying
x = -0.763932022


Subproblem 2
x + 3 = -2.236067978

Simplifying
x + 3 = -2.236067978

Reorder the terms:
3 + x = -2.236067978

Solving
3 + x = -2.236067978

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.236067978 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.236067978 + -3
x = -2.236067978 + -3

Combine like terms: -2.236067978 + -3 = -5.236067978
x = -5.236067978

Simplifying
x = -5.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.763932022, -5.236067978}
Solution
x = {-0.763932022, -5.236067978}

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