2x^2-26x-14=0

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Solution for 2x^2-26x-14=0 equation: 


Simplifying
2x2 + -26x + -14 = 0

Reorder the terms:
-14 + -26x + 2x2 = 0

Solving
-14 + -26x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -13x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -13x + x2 = 0

Solving
-7 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -13x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -13x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13x + x2 = 0 + 7
-13x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-13x + x2 = 7

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 7 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 7 + 42.25

Combine like terms: 7 + 42.25 = 49.25
42.25 + -13x + x2 = 49.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + -6.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
x + -6.5 = 7.017834424

Simplifying
x + -6.5 = 7.017834424

Reorder the terms:
-6.5 + x = 7.017834424

Solving
-6.5 + x = 7.017834424

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 7.017834424 + 6.5
x = 7.017834424 + 6.5

Combine like terms: 7.017834424 + 6.5 = 13.517834424
x = 13.517834424

Simplifying
x = 13.517834424


Subproblem 2
x + -6.5 = -7.017834424

Simplifying
x + -6.5 = -7.017834424

Reorder the terms:
-6.5 + x = -7.017834424

Solving
-6.5 + x = -7.017834424

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -7.017834424 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -7.017834424 + 6.5
x = -7.017834424 + 6.5

Combine like terms: -7.017834424 + 6.5 = -0.517834424
x = -0.517834424

Simplifying
x = -0.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.517834424, -0.517834424}
Solution
x = {13.517834424, -0.517834424}

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