x^2-5x-27=0

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Solution for x^2-5x-27=0 equation: 


Simplifying
x2 + -5x + -27 = 0

Reorder the terms:
-27 + -5x + x2 = 0

Solving
-27 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -5x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -5x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -5x + x2 = 0 + 27
-5x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-5x + x2 = 27

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 27 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 27 + 6.25

Combine like terms: 27 + 6.25 = 33.25
6.25 + -5x + x2 = 33.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + -2.5) equal to 5.766281297 and -5.766281297.


Subproblem 1
x + -2.5 = 5.766281297

Simplifying
x + -2.5 = 5.766281297

Reorder the terms:
-2.5 + x = 5.766281297

Solving
-2.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 5.766281297 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 5.766281297 + 2.5
x = 5.766281297 + 2.5

Combine like terms: 5.766281297 + 2.5 = 8.266281297
x = 8.266281297

Simplifying
x = 8.266281297


Subproblem 2
x + -2.5 = -5.766281297

Simplifying
x + -2.5 = -5.766281297

Reorder the terms:
-2.5 + x = -5.766281297

Solving
-2.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -5.766281297 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -5.766281297 + 2.5
x = -5.766281297 + 2.5

Combine like terms: -5.766281297 + 2.5 = -3.266281297
x = -3.266281297

Simplifying
x = -3.266281297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.266281297, -3.266281297}

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