3x^2+31x-10=0

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Solution for 3x^2+31x-10=0 equation: 


Simplifying
3x2 + 31x + -10 = 0

Reorder the terms:
-10 + 31x + 3x2 = 0

Solving
-10 + 31x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.333333333 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 10.33333333x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 10.33333333x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + 3.333333333
10.33333333x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
10.33333333x + x2 = 3.333333333

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = 3.333333333 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 3.333333333 + 26.69444443

Combine like terms: 3.333333333 + 26.69444443 = 30.027777763
26.69444443 + 10.33333333x + x2 = 30.027777763

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 30.027777763

Calculate the square root of the right side: 5.47976074

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.47976074 and -5.47976074.


Subproblem 1
x + 5.166666665 = 5.47976074

Simplifying
x + 5.166666665 = 5.47976074

Reorder the terms:
5.166666665 + x = 5.47976074

Solving
5.166666665 + x = 5.47976074

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 5.47976074 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 5.47976074 + -5.166666665
x = 5.47976074 + -5.166666665

Combine like terms: 5.47976074 + -5.166666665 = 0.313094075
x = 0.313094075

Simplifying
x = 0.313094075


Subproblem 2
x + 5.166666665 = -5.47976074

Simplifying
x + 5.166666665 = -5.47976074

Reorder the terms:
5.166666665 + x = -5.47976074

Solving
5.166666665 + x = -5.47976074

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -5.47976074 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -5.47976074 + -5.166666665
x = -5.47976074 + -5.166666665

Combine like terms: -5.47976074 + -5.166666665 = -10.646427405
x = -10.646427405

Simplifying
x = -10.646427405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.313094075, -10.646427405}

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