x^2+14x-8=0

Solution for x^2+14x-8=0 equation:

Simplifying
x2 + 14x + -8 = 0

Reorder the terms:
-8 + 14x + x2 = 0

Solving
-8 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 14x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 14x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 14x + x2 = 0 + 8
14x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
14x + x2 = 8

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 = 8 + 49

Reorder the terms:
49 + 14x + x2 = 8 + 49

Combine like terms: 8 + 49 = 57
49 + 14x + x2 = 57

Factor a perfect square on the left side:
(x + 7)(x + 7) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 7) equal to 7.549834435 and -7.549834435.

Subproblem 1
x + 7 = 7.549834435

Simplifying
x + 7 = 7.549834435

Reorder the terms:
7 + x = 7.549834435

Solving
7 + x = 7.549834435

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 = 7.549834435 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.549834435 + -7
x = 7.549834435 + -7

Combine like terms: 7.549834435 + -7 = 0.549834435
x = 0.549834435

Simplifying
x = 0.549834435

Subproblem 2
x + 7 = -7.549834435

Simplifying
x + 7 = -7.549834435

Reorder the terms:
7 + x = -7.549834435

Solving
7 + x = -7.549834435

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 = -7.549834435 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.549834435 + -7
x = -7.549834435 + -7

Combine like terms: -7.549834435 + -7 = -14.549834435
x = -14.549834435

Simplifying
x = -14.549834435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.549834435, -14.549834435}