7x^2+14x+6=0

Solution for 7x^2+14x+6=0 equation:

Simplifying
7x2 + 14x + 6 = 0

Reorder the terms:
6 + 14x + 7x2 = 0

Solving
6 + 14x + 7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.8571428571 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 2x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 2x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.8571428571
2x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
2x + x2 = -0.8571428571

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.8571428571 + 1

Reorder the terms:
1 + 2x + x2 = -0.8571428571 + 1

Combine like terms: -0.8571428571 + 1 = 0.1428571429
1 + 2x + x2 = 0.1428571429

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.1428571429

Calculate the square root of the right side: 0.377964473

Break this problem into two subproblems by setting 
(x + 1) equal to 0.377964473 and -0.377964473.

Subproblem 1
x + 1 = 0.377964473

Simplifying
x + 1 = 0.377964473

Reorder the terms:
1 + x = 0.377964473

Solving
1 + x = 0.377964473

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.377964473 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.377964473 + -1
x = 0.377964473 + -1

Combine like terms: 0.377964473 + -1 = -0.622035527
x = -0.622035527

Simplifying
x = -0.622035527

Subproblem 2
x + 1 = -0.377964473

Simplifying
x + 1 = -0.377964473

Reorder the terms:
1 + x = -0.377964473

Solving
1 + x = -0.377964473

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.377964473 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.377964473 + -1
x = -0.377964473 + -1

Combine like terms: -0.377964473 + -1 = -1.377964473
x = -1.377964473

Simplifying
x = -1.377964473

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.622035527, -1.377964473}