-2x^2-13x-5=0

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Solution for -2x^2-13x-5=0 equation:


Simplifying
-2x2 + -13x + -5 = 0

Reorder the terms:
-5 + -13x + -2x2 = 0

Solving
-5 + -13x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 13x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + 13x + 2x2 = 0

Solving
5 + 13x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 6.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 6.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 6.5x + x2 = 0 + -2.5
6.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
6.5x + x2 = -2.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -2.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -2.5 + 10.5625

Combine like terms: -2.5 + 10.5625 = 8.0625
10.5625 + 6.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + 3.25) equal to 2.839454173 and -2.839454173.


Subproblem 1
x + 3.25 = 2.839454173

Simplifying
x + 3.25 = 2.839454173

Reorder the terms:
3.25 + x = 2.839454173

Solving
3.25 + x = 2.839454173

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 2.839454173 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 2.839454173 + -3.25
x = 2.839454173 + -3.25

Combine like terms: 2.839454173 + -3.25 = -0.410545827
x = -0.410545827

Simplifying
x = -0.410545827


Subproblem 2
x + 3.25 = -2.839454173

Simplifying
x + 3.25 = -2.839454173

Reorder the terms:
3.25 + x = -2.839454173

Solving
3.25 + x = -2.839454173

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -2.839454173 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -2.839454173 + -3.25
x = -2.839454173 + -3.25

Combine like terms: -2.839454173 + -3.25 = -6.089454173
x = -6.089454173

Simplifying
x = -6.089454173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.410545827, -6.089454173}
Solution
x = {-0.410545827, -6.089454173}

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