x^2-14x-27=0

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Solution for x^2-14x-27=0 equation: 


Simplifying
x2 + -14x + -27 = 0

Reorder the terms:
-27 + -14x + x2 = 0

Solving
-27 + -14x + 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 + -14x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -14x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -14x + x2 = 0 + 27
-14x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-14x + x2 = 27

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 = 27 + 49

Reorder the terms:
49 + -14x + x2 = 27 + 49

Combine like terms: 27 + 49 = 76
49 + -14x + x2 = 76

Factor a perfect square on the left side:
(x + -7)(x + -7) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -7) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + -7 = 8.717797887

Simplifying
x + -7 = 8.717797887

Reorder the terms:
-7 + x = 8.717797887

Solving
-7 + x = 8.717797887

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 = 8.717797887 + 7

Combine like terms: -7 + 7 = 0
0 + x = 8.717797887 + 7
x = 8.717797887 + 7

Combine like terms: 8.717797887 + 7 = 15.717797887
x = 15.717797887

Simplifying
x = 15.717797887


Subproblem 2
x + -7 = -8.717797887

Simplifying
x + -7 = -8.717797887

Reorder the terms:
-7 + x = -8.717797887

Solving
-7 + x = -8.717797887

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 = -8.717797887 + 7

Combine like terms: -7 + 7 = 0
0 + x = -8.717797887 + 7
x = -8.717797887 + 7

Combine like terms: -8.717797887 + 7 = -1.717797887
x = -1.717797887

Simplifying
x = -1.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.717797887, -1.717797887}

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