3x^2+31x-4=0

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Solution for 3x^2+31x-4=0 equation: 


Simplifying
3x2 + 31x + -4 = 0

Reorder the terms:
-4 + 31x + 3x2 = 0

Solving
-4 + 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'.
-1.333333333 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 10.33333333x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 10.33333333x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + 1.333333333
10.33333333x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
10.33333333x + x2 = 1.333333333

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 = 1.333333333 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 1.333333333 + 26.69444443

Combine like terms: 1.333333333 + 26.69444443 = 28.027777763
26.69444443 + 10.33333333x + x2 = 28.027777763

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 28.027777763

Calculate the square root of the right side: 5.294126723

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.294126723 and -5.294126723.


Subproblem 1
x + 5.166666665 = 5.294126723

Simplifying
x + 5.166666665 = 5.294126723

Reorder the terms:
5.166666665 + x = 5.294126723

Solving
5.166666665 + x = 5.294126723

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 = 5.294126723 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 5.294126723 + -5.166666665
x = 5.294126723 + -5.166666665

Combine like terms: 5.294126723 + -5.166666665 = 0.127460058
x = 0.127460058

Simplifying
x = 0.127460058


Subproblem 2
x + 5.166666665 = -5.294126723

Simplifying
x + 5.166666665 = -5.294126723

Reorder the terms:
5.166666665 + x = -5.294126723

Solving
5.166666665 + x = -5.294126723

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 = -5.294126723 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -5.294126723 + -5.166666665
x = -5.294126723 + -5.166666665

Combine like terms: -5.294126723 + -5.166666665 = -10.460793388
x = -10.460793388

Simplifying
x = -10.460793388


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.127460058, -10.460793388}

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