x^2-14x-1920=0

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Solution for x^2-14x-1920=0 equation: 


Simplifying
x2 + -14x + -1920 = 0

Reorder the terms:
-1920 + -14x + x2 = 0

Solving
-1920 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1920' to each side of the equation.
-1920 + -14x + 1920 + x2 = 0 + 1920

Reorder the terms:
-1920 + 1920 + -14x + x2 = 0 + 1920

Combine like terms: -1920 + 1920 = 0
0 + -14x + x2 = 0 + 1920
-14x + x2 = 0 + 1920

Combine like terms: 0 + 1920 = 1920
-14x + x2 = 1920

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 = 1920 + 49

Reorder the terms:
49 + -14x + x2 = 1920 + 49

Combine like terms: 1920 + 49 = 1969
49 + -14x + x2 = 1969

Factor a perfect square on the left side:
(x + -7)(x + -7) = 1969

Calculate the square root of the right side: 44.373415465

Break this problem into two subproblems by setting 
(x + -7) equal to 44.373415465 and -44.373415465.


Subproblem 1
x + -7 = 44.373415465

Simplifying
x + -7 = 44.373415465

Reorder the terms:
-7 + x = 44.373415465

Solving
-7 + x = 44.373415465

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 = 44.373415465 + 7

Combine like terms: -7 + 7 = 0
0 + x = 44.373415465 + 7
x = 44.373415465 + 7

Combine like terms: 44.373415465 + 7 = 51.373415465
x = 51.373415465

Simplifying
x = 51.373415465


Subproblem 2
x + -7 = -44.373415465

Simplifying
x + -7 = -44.373415465

Reorder the terms:
-7 + x = -44.373415465

Solving
-7 + x = -44.373415465

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 = -44.373415465 + 7

Combine like terms: -7 + 7 = 0
0 + x = -44.373415465 + 7
x = -44.373415465 + 7

Combine like terms: -44.373415465 + 7 = -37.373415465
x = -37.373415465

Simplifying
x = -37.373415465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {51.373415465, -37.373415465}

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