2x^2-14x-231=0

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Solution for 2x^2-14x-231=0 equation: 


Simplifying
2x2 + -14x + -231 = 0

Reorder the terms:
-231 + -14x + 2x2 = 0

Solving
-231 + -14x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-115.5 + -7x + x2 = 0

Move the constant term to the right:

Add '115.5' to each side of the equation.
-115.5 + -7x + 115.5 + x2 = 0 + 115.5

Reorder the terms:
-115.5 + 115.5 + -7x + x2 = 0 + 115.5

Combine like terms: -115.5 + 115.5 = 0.0
0.0 + -7x + x2 = 0 + 115.5
-7x + x2 = 0 + 115.5

Combine like terms: 0 + 115.5 = 115.5
-7x + x2 = 115.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 115.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 115.5 + 12.25

Combine like terms: 115.5 + 12.25 = 127.75
12.25 + -7x + x2 = 127.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 127.75

Calculate the square root of the right side: 11.302654555

Break this problem into two subproblems by setting 
(x + -3.5) equal to 11.302654555 and -11.302654555.


Subproblem 1
x + -3.5 = 11.302654555

Simplifying
x + -3.5 = 11.302654555

Reorder the terms:
-3.5 + x = 11.302654555

Solving
-3.5 + x = 11.302654555

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 11.302654555 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 11.302654555 + 3.5
x = 11.302654555 + 3.5

Combine like terms: 11.302654555 + 3.5 = 14.802654555
x = 14.802654555

Simplifying
x = 14.802654555


Subproblem 2
x + -3.5 = -11.302654555

Simplifying
x + -3.5 = -11.302654555

Reorder the terms:
-3.5 + x = -11.302654555

Solving
-3.5 + x = -11.302654555

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -11.302654555 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -11.302654555 + 3.5
x = -11.302654555 + 3.5

Combine like terms: -11.302654555 + 3.5 = -7.802654555
x = -7.802654555

Simplifying
x = -7.802654555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.802654555, -7.802654555}

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