6x^2+31x-18=

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Solution for 6x^2+31x-18= equation: 


Simplifying
6x2 + 31x + -18 = 0

Reorder the terms:
-18 + 31x + 6x2 = 0

Solving
-18 + 31x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-3 + 5.166666667x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5.166666667x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 5.166666667x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5.166666667x + x2 = 0 + 3
5.166666667x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
5.166666667x + x2 = 3

The x term is 5.166666667x.  Take half its coefficient (2.583333334).
Square it (6.673611115) and add it to both sides.

Add '6.673611115' to each side of the equation.
5.166666667x + 6.673611115 + x2 = 3 + 6.673611115

Reorder the terms:
6.673611115 + 5.166666667x + x2 = 3 + 6.673611115

Combine like terms: 3 + 6.673611115 = 9.673611115
6.673611115 + 5.166666667x + x2 = 9.673611115

Factor a perfect square on the left side:
(x + 2.583333334)(x + 2.583333334) = 9.673611115

Calculate the square root of the right side: 3.110242935

Break this problem into two subproblems by setting 
(x + 2.583333334) equal to 3.110242935 and -3.110242935.


Subproblem 1
x + 2.583333334 = 3.110242935

Simplifying
x + 2.583333334 = 3.110242935

Reorder the terms:
2.583333334 + x = 3.110242935

Solving
2.583333334 + x = 3.110242935

Solving for variable 'x'.

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

Add '-2.583333334' to each side of the equation.
2.583333334 + -2.583333334 + x = 3.110242935 + -2.583333334

Combine like terms: 2.583333334 + -2.583333334 = 0.000000000
0.000000000 + x = 3.110242935 + -2.583333334
x = 3.110242935 + -2.583333334

Combine like terms: 3.110242935 + -2.583333334 = 0.526909601
x = 0.526909601

Simplifying
x = 0.526909601


Subproblem 2
x + 2.583333334 = -3.110242935

Simplifying
x + 2.583333334 = -3.110242935

Reorder the terms:
2.583333334 + x = -3.110242935

Solving
2.583333334 + x = -3.110242935

Solving for variable 'x'.

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

Add '-2.583333334' to each side of the equation.
2.583333334 + -2.583333334 + x = -3.110242935 + -2.583333334

Combine like terms: 2.583333334 + -2.583333334 = 0.000000000
0.000000000 + x = -3.110242935 + -2.583333334
x = -3.110242935 + -2.583333334

Combine like terms: -3.110242935 + -2.583333334 = -5.693576269
x = -5.693576269

Simplifying
x = -5.693576269


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.526909601, -5.693576269}

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