x^2-14x-331=0

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Solution for x^2-14x-331=0 equation: 


Simplifying
x2 + -14x + -331 = 0

Reorder the terms:
-331 + -14x + x2 = 0

Solving
-331 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '331' to each side of the equation.
-331 + -14x + 331 + x2 = 0 + 331

Reorder the terms:
-331 + 331 + -14x + x2 = 0 + 331

Combine like terms: -331 + 331 = 0
0 + -14x + x2 = 0 + 331
-14x + x2 = 0 + 331

Combine like terms: 0 + 331 = 331
-14x + x2 = 331

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 = 331 + 49

Reorder the terms:
49 + -14x + x2 = 331 + 49

Combine like terms: 331 + 49 = 380
49 + -14x + x2 = 380

Factor a perfect square on the left side:
(x + -7)(x + -7) = 380

Calculate the square root of the right side: 19.49358869

Break this problem into two subproblems by setting 
(x + -7) equal to 19.49358869 and -19.49358869.


Subproblem 1
x + -7 = 19.49358869

Simplifying
x + -7 = 19.49358869

Reorder the terms:
-7 + x = 19.49358869

Solving
-7 + x = 19.49358869

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 = 19.49358869 + 7

Combine like terms: -7 + 7 = 0
0 + x = 19.49358869 + 7
x = 19.49358869 + 7

Combine like terms: 19.49358869 + 7 = 26.49358869
x = 26.49358869

Simplifying
x = 26.49358869


Subproblem 2
x + -7 = -19.49358869

Simplifying
x + -7 = -19.49358869

Reorder the terms:
-7 + x = -19.49358869

Solving
-7 + x = -19.49358869

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 = -19.49358869 + 7

Combine like terms: -7 + 7 = 0
0 + x = -19.49358869 + 7
x = -19.49358869 + 7

Combine like terms: -19.49358869 + 7 = -12.49358869
x = -12.49358869

Simplifying
x = -12.49358869


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.49358869, -12.49358869}

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