2x^2+31x-5.9=0

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Solution for 2x^2+31x-5.9=0 equation: 


Simplifying
2x2 + 31x + -5.9 = 0

Reorder the terms:
-5.9 + 31x + 2x2 = 0

Solving
-5.9 + 31x + 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'.
-2.95 + 15.5x + x2 = 0

Move the constant term to the right:

Add '2.95' to each side of the equation.
-2.95 + 15.5x + 2.95 + x2 = 0 + 2.95

Reorder the terms:
-2.95 + 2.95 + 15.5x + x2 = 0 + 2.95

Combine like terms: -2.95 + 2.95 = 0.00
0.00 + 15.5x + x2 = 0 + 2.95
15.5x + x2 = 0 + 2.95

Combine like terms: 0 + 2.95 = 2.95
15.5x + x2 = 2.95

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = 2.95 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 2.95 + 60.0625

Combine like terms: 2.95 + 60.0625 = 63.0125
60.0625 + 15.5x + x2 = 63.0125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 63.0125

Calculate the square root of the right side: 7.93804132

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.93804132 and -7.93804132.


Subproblem 1
x + 7.75 = 7.93804132

Simplifying
x + 7.75 = 7.93804132

Reorder the terms:
7.75 + x = 7.93804132

Solving
7.75 + x = 7.93804132

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 7.93804132 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 7.93804132 + -7.75
x = 7.93804132 + -7.75

Combine like terms: 7.93804132 + -7.75 = 0.18804132
x = 0.18804132

Simplifying
x = 0.18804132


Subproblem 2
x + 7.75 = -7.93804132

Simplifying
x + 7.75 = -7.93804132

Reorder the terms:
7.75 + x = -7.93804132

Solving
7.75 + x = -7.93804132

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -7.93804132 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -7.93804132 + -7.75
x = -7.93804132 + -7.75

Combine like terms: -7.93804132 + -7.75 = -15.68804132
x = -15.68804132

Simplifying
x = -15.68804132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.18804132, -15.68804132}

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