x^2-8.5x-255=0

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Solution for x^2-8.5x-255=0 equation: 


Simplifying
x2 + -8.5x + -255 = 0

Reorder the terms:
-255 + -8.5x + x2 = 0

Solving
-255 + -8.5x + 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 + -8.5x + 255 + x2 = 0 + 255

Reorder the terms:
-255 + 255 + -8.5x + x2 = 0 + 255

Combine like terms: -255 + 255 = 0
0 + -8.5x + x2 = 0 + 255
-8.5x + x2 = 0 + 255

Combine like terms: 0 + 255 = 255
-8.5x + x2 = 255

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 255 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 255 + 18.0625

Combine like terms: 255 + 18.0625 = 273.0625
18.0625 + -8.5x + x2 = 273.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 273.0625

Calculate the square root of the right side: 16.52460287

Break this problem into two subproblems by setting 
(x + -4.25) equal to 16.52460287 and -16.52460287.


Subproblem 1
x + -4.25 = 16.52460287

Simplifying
x + -4.25 = 16.52460287

Reorder the terms:
-4.25 + x = 16.52460287

Solving
-4.25 + x = 16.52460287

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 16.52460287 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 16.52460287 + 4.25
x = 16.52460287 + 4.25

Combine like terms: 16.52460287 + 4.25 = 20.77460287
x = 20.77460287

Simplifying
x = 20.77460287


Subproblem 2
x + -4.25 = -16.52460287

Simplifying
x + -4.25 = -16.52460287

Reorder the terms:
-4.25 + x = -16.52460287

Solving
-4.25 + x = -16.52460287

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -16.52460287 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -16.52460287 + 4.25
x = -16.52460287 + 4.25

Combine like terms: -16.52460287 + 4.25 = -12.27460287
x = -12.27460287

Simplifying
x = -12.27460287


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.77460287, -12.27460287}

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