x^2-14x-7=0

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Solution for x^2-14x-7=0 equation: 


Simplifying
x2 + -14x + -7 = 0

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

Solving
-7 + -14x + 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 + -14x + 7 + x2 = 0 + 7

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

Combine like terms: -7 + 7 = 0
0 + -14x + x2 = 0 + 7
-14x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-14x + x2 = 7

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 = 7 + 49

Reorder the terms:
49 + -14x + x2 = 7 + 49

Combine like terms: 7 + 49 = 56
49 + -14x + x2 = 56

Factor a perfect square on the left side:
(x + -7)(x + -7) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -7) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + -7 = 7.483314774

Simplifying
x + -7 = 7.483314774

Reorder the terms:
-7 + x = 7.483314774

Solving
-7 + x = 7.483314774

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 = 7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.483314774 + 7
x = 7.483314774 + 7

Combine like terms: 7.483314774 + 7 = 14.483314774
x = 14.483314774

Simplifying
x = 14.483314774


Subproblem 2
x + -7 = -7.483314774

Simplifying
x + -7 = -7.483314774

Reorder the terms:
-7 + x = -7.483314774

Solving
-7 + x = -7.483314774

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 = -7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.483314774 + 7
x = -7.483314774 + 7

Combine like terms: -7.483314774 + 7 = -0.483314774
x = -0.483314774

Simplifying
x = -0.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.483314774, -0.483314774}

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