3x^2+31x-9.1=0

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Solution for 3x^2+31x-9.1=0 equation: 


Simplifying
3x2 + 31x + -9.1 = 0

Reorder the terms:
-9.1 + 31x + 3x2 = 0

Solving
-9.1 + 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'.
-3.033333333 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '3.033333333' to each side of the equation.
-3.033333333 + 10.33333333x + 3.033333333 + x2 = 0 + 3.033333333

Reorder the terms:
-3.033333333 + 3.033333333 + 10.33333333x + x2 = 0 + 3.033333333

Combine like terms: -3.033333333 + 3.033333333 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + 3.033333333
10.33333333x + x2 = 0 + 3.033333333

Combine like terms: 0 + 3.033333333 = 3.033333333
10.33333333x + x2 = 3.033333333

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 = 3.033333333 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 3.033333333 + 26.69444443

Combine like terms: 3.033333333 + 26.69444443 = 29.727777763
26.69444443 + 10.33333333x + x2 = 29.727777763

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 29.727777763

Calculate the square root of the right side: 5.452318568

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.452318568 and -5.452318568.


Subproblem 1
x + 5.166666665 = 5.452318568

Simplifying
x + 5.166666665 = 5.452318568

Reorder the terms:
5.166666665 + x = 5.452318568

Solving
5.166666665 + x = 5.452318568

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 = 5.452318568 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 5.452318568 + -5.166666665
x = 5.452318568 + -5.166666665

Combine like terms: 5.452318568 + -5.166666665 = 0.285651903
x = 0.285651903

Simplifying
x = 0.285651903


Subproblem 2
x + 5.166666665 = -5.452318568

Simplifying
x + 5.166666665 = -5.452318568

Reorder the terms:
5.166666665 + x = -5.452318568

Solving
5.166666665 + x = -5.452318568

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 = -5.452318568 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -5.452318568 + -5.166666665
x = -5.452318568 + -5.166666665

Combine like terms: -5.452318568 + -5.166666665 = -10.618985233
x = -10.618985233

Simplifying
x = -10.618985233


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.285651903, -10.618985233}

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