3x^2+31x-8.1=0

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Solution for 3x^2+31x-8.1=0 equation: 


Simplifying
3x2 + 31x + -8.1 = 0

Reorder the terms:
-8.1 + 31x + 3x2 = 0

Solving
-8.1 + 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'.
-2.7 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '2.7' to each side of the equation.
-2.7 + 10.33333333x + 2.7 + x2 = 0 + 2.7

Reorder the terms:
-2.7 + 2.7 + 10.33333333x + x2 = 0 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + 10.33333333x + x2 = 0 + 2.7
10.33333333x + x2 = 0 + 2.7

Combine like terms: 0 + 2.7 = 2.7
10.33333333x + x2 = 2.7

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 = 2.7 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 2.7 + 26.69444443

Combine like terms: 2.7 + 26.69444443 = 29.39444443
26.69444443 + 10.33333333x + x2 = 29.39444443

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 29.39444443

Calculate the square root of the right side: 5.42166436

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.42166436 and -5.42166436.


Subproblem 1
x + 5.166666665 = 5.42166436

Simplifying
x + 5.166666665 = 5.42166436

Reorder the terms:
5.166666665 + x = 5.42166436

Solving
5.166666665 + x = 5.42166436

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 = 5.42166436 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 5.42166436 + -5.166666665
x = 5.42166436 + -5.166666665

Combine like terms: 5.42166436 + -5.166666665 = 0.254997695
x = 0.254997695

Simplifying
x = 0.254997695


Subproblem 2
x + 5.166666665 = -5.42166436

Simplifying
x + 5.166666665 = -5.42166436

Reorder the terms:
5.166666665 + x = -5.42166436

Solving
5.166666665 + x = -5.42166436

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 = -5.42166436 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -5.42166436 + -5.166666665
x = -5.42166436 + -5.166666665

Combine like terms: -5.42166436 + -5.166666665 = -10.588331025
x = -10.588331025

Simplifying
x = -10.588331025


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.254997695, -10.588331025}

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