x^2+6x+7=0

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Solution for x^2+6x+7=0 equation: 


Simplifying
x2 + 6x + 7 = 0

Reorder the terms:
7 + 6x + x2 = 0

Solving
7 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x + x2 = 0 + -7
6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
6x + x2 = -7

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 = -7 + 9

Reorder the terms:
9 + 6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + 6x + x2 = 2

Factor a perfect square on the left side:
(x + 3)(x + 3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 3) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 3 = 1.414213562

Simplifying
x + 3 = 1.414213562

Reorder the terms:
3 + x = 1.414213562

Solving
3 + x = 1.414213562

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 = 1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.414213562 + -3
x = 1.414213562 + -3

Combine like terms: 1.414213562 + -3 = -1.585786438
x = -1.585786438

Simplifying
x = -1.585786438


Subproblem 2
x + 3 = -1.414213562

Simplifying
x + 3 = -1.414213562

Reorder the terms:
3 + x = -1.414213562

Solving
3 + x = -1.414213562

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 = -1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.414213562 + -3
x = -1.414213562 + -3

Combine like terms: -1.414213562 + -3 = -4.414213562
x = -4.414213562

Simplifying
x = -4.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.585786438, -4.414213562}

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