x^2-14x-216=0

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Solution for x^2-14x-216=0 equation: 


Simplifying
x2 + -14x + -216 = 0

Reorder the terms:
-216 + -14x + x2 = 0

Solving
-216 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + -14x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + -14x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + -14x + x2 = 0 + 216
-14x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
-14x + x2 = 216

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 = 216 + 49

Reorder the terms:
49 + -14x + x2 = 216 + 49

Combine like terms: 216 + 49 = 265
49 + -14x + x2 = 265

Factor a perfect square on the left side:
(x + -7)(x + -7) = 265

Calculate the square root of the right side: 16.278820596

Break this problem into two subproblems by setting 
(x + -7) equal to 16.278820596 and -16.278820596.


Subproblem 1
x + -7 = 16.278820596

Simplifying
x + -7 = 16.278820596

Reorder the terms:
-7 + x = 16.278820596

Solving
-7 + x = 16.278820596

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 = 16.278820596 + 7

Combine like terms: -7 + 7 = 0
0 + x = 16.278820596 + 7
x = 16.278820596 + 7

Combine like terms: 16.278820596 + 7 = 23.278820596
x = 23.278820596

Simplifying
x = 23.278820596


Subproblem 2
x + -7 = -16.278820596

Simplifying
x + -7 = -16.278820596

Reorder the terms:
-7 + x = -16.278820596

Solving
-7 + x = -16.278820596

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 = -16.278820596 + 7

Combine like terms: -7 + 7 = 0
0 + x = -16.278820596 + 7
x = -16.278820596 + 7

Combine like terms: -16.278820596 + 7 = -9.278820596
x = -9.278820596

Simplifying
x = -9.278820596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.278820596, -9.278820596}

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