x^2-14x-65=0

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Solution for x^2-14x-65=0 equation: 


Simplifying
x2 + -14x + -65 = 0

Reorder the terms:
-65 + -14x + x2 = 0

Solving
-65 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -14x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + -14x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -14x + x2 = 0 + 65
-14x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
-14x + x2 = 65

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 = 65 + 49

Reorder the terms:
49 + -14x + x2 = 65 + 49

Combine like terms: 65 + 49 = 114
49 + -14x + x2 = 114

Factor a perfect square on the left side:
(x + -7)(x + -7) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + -7) equal to 10.677078252 and -10.677078252.


Subproblem 1
x + -7 = 10.677078252

Simplifying
x + -7 = 10.677078252

Reorder the terms:
-7 + x = 10.677078252

Solving
-7 + x = 10.677078252

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 = 10.677078252 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.677078252 + 7
x = 10.677078252 + 7

Combine like terms: 10.677078252 + 7 = 17.677078252
x = 17.677078252

Simplifying
x = 17.677078252


Subproblem 2
x + -7 = -10.677078252

Simplifying
x + -7 = -10.677078252

Reorder the terms:
-7 + x = -10.677078252

Solving
-7 + x = -10.677078252

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 = -10.677078252 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.677078252 + 7
x = -10.677078252 + 7

Combine like terms: -10.677078252 + 7 = -3.677078252
x = -3.677078252

Simplifying
x = -3.677078252


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.677078252, -3.677078252}

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