x^2-14x-255=0

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Solution for x^2-14x-255=0 equation: 


Simplifying
x2 + -14x + -255 = 0

Reorder the terms:
-255 + -14x + x2 = 0

Solving
-255 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '255' to each side of the equation.
-255 + -14x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + -14x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + -14x + x2 = 0 + 255
-14x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
-14x + x2 = 255

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 = 255 + 49

Reorder the terms:
49 + -14x + x2 = 255 + 49

Combine like terms: 255 + 49 = 304
49 + -14x + x2 = 304

Factor a perfect square on the left side:
(x + -7)(x + -7) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(x + -7) equal to 17.435595774 and -17.435595774.


Subproblem 1
x + -7 = 17.435595774

Simplifying
x + -7 = 17.435595774

Reorder the terms:
-7 + x = 17.435595774

Solving
-7 + x = 17.435595774

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 = 17.435595774 + 7

Combine like terms: -7 + 7 = 0
0 + x = 17.435595774 + 7
x = 17.435595774 + 7

Combine like terms: 17.435595774 + 7 = 24.435595774
x = 24.435595774

Simplifying
x = 24.435595774


Subproblem 2
x + -7 = -17.435595774

Simplifying
x + -7 = -17.435595774

Reorder the terms:
-7 + x = -17.435595774

Solving
-7 + x = -17.435595774

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 = -17.435595774 + 7

Combine like terms: -7 + 7 = 0
0 + x = -17.435595774 + 7
x = -17.435595774 + 7

Combine like terms: -17.435595774 + 7 = -10.435595774
x = -10.435595774

Simplifying
x = -10.435595774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.435595774, -10.435595774}

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