x^2+14x-3=0

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

Simplifying
x2 + 14x + -3 = 0

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

Solving
-3 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 14x + 3 + x2 = 0 + 3

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

Combine like terms: -3 + 3 = 0
0 + 14x + x2 = 0 + 3
14x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
14x + x2 = 3

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 3 + 49

Reorder the terms:
49 + 14x + x2 = 3 + 49

Combine like terms: 3 + 49 = 52
49 + 14x + x2 = 52

Factor a perfect square on the left side:
(x + 7)(x + 7) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 7) equal to 7.211102551 and -7.211102551.

Subproblem 1
x + 7 = 7.211102551

Simplifying
x + 7 = 7.211102551

Reorder the terms:
7 + x = 7.211102551

Solving
7 + x = 7.211102551

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 7.211102551 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.211102551 + -7
x = 7.211102551 + -7

Combine like terms: 7.211102551 + -7 = 0.211102551
x = 0.211102551

Simplifying
x = 0.211102551

Subproblem 2
x + 7 = -7.211102551

Simplifying
x + 7 = -7.211102551

Reorder the terms:
7 + x = -7.211102551

Solving
7 + x = -7.211102551

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -7.211102551 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.211102551 + -7
x = -7.211102551 + -7

Combine like terms: -7.211102551 + -7 = -14.211102551
x = -14.211102551

Simplifying
x = -14.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.211102551, -14.211102551}