7x^2+14x+3=0

Solution for 7x^2+14x+3=0 equation:

Simplifying
7x2 + 14x + 3 = 0

Reorder the terms:
3 + 14x + 7x2 = 0

Solving
3 + 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'.
0.4285714286 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + 2x + -0.4285714286 + x2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + 2x + x2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.4285714286
2x + x2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
2x + x2 = -0.4285714286

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 = -0.4285714286 + 1

Reorder the terms:
1 + 2x + x2 = -0.4285714286 + 1

Combine like terms: -0.4285714286 + 1 = 0.5714285714
1 + 2x + x2 = 0.5714285714

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.5714285714

Calculate the square root of the right side: 0.755928946

Break this problem into two subproblems by setting 
(x + 1) equal to 0.755928946 and -0.755928946.

Subproblem 1
x + 1 = 0.755928946

Simplifying
x + 1 = 0.755928946

Reorder the terms:
1 + x = 0.755928946

Solving
1 + x = 0.755928946

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 = 0.755928946 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.755928946 + -1
x = 0.755928946 + -1

Combine like terms: 0.755928946 + -1 = -0.244071054
x = -0.244071054

Simplifying
x = -0.244071054

Subproblem 2
x + 1 = -0.755928946

Simplifying
x + 1 = -0.755928946

Reorder the terms:
1 + x = -0.755928946

Solving
1 + x = -0.755928946

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 = -0.755928946 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.755928946 + -1
x = -0.755928946 + -1

Combine like terms: -0.755928946 + -1 = -1.755928946
x = -1.755928946

Simplifying
x = -1.755928946

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.244071054, -1.755928946}