6x^2-2x-325=0

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Solution for 6x^2-2x-325=0 equation: 


Simplifying
6x2 + -2x + -325 = 0

Reorder the terms:
-325 + -2x + 6x2 = 0

Solving
-325 + -2x + 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'.
-54.16666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '54.16666667' to each side of the equation.
-54.16666667 + -0.3333333333x + 54.16666667 + x2 = 0 + 54.16666667

Reorder the terms:
-54.16666667 + 54.16666667 + -0.3333333333x + x2 = 0 + 54.16666667

Combine like terms: -54.16666667 + 54.16666667 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + 54.16666667
-0.3333333333x + x2 = 0 + 54.16666667

Combine like terms: 0 + 54.16666667 = 54.16666667
-0.3333333333x + x2 = 54.16666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 54.16666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 54.16666667 + 0.02777777779

Combine like terms: 54.16666667 + 0.02777777779 = 54.19444444779
0.02777777779 + -0.3333333333x + x2 = 54.19444444779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 54.19444444779

Calculate the square root of the right side: 7.361687609

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 7.361687609 and -7.361687609.


Subproblem 1
x + -0.1666666667 = 7.361687609

Simplifying
x + -0.1666666667 = 7.361687609

Reorder the terms:
-0.1666666667 + x = 7.361687609

Solving
-0.1666666667 + x = 7.361687609

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 7.361687609 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 7.361687609 + 0.1666666667
x = 7.361687609 + 0.1666666667

Combine like terms: 7.361687609 + 0.1666666667 = 7.5283542757
x = 7.5283542757

Simplifying
x = 7.5283542757


Subproblem 2
x + -0.1666666667 = -7.361687609

Simplifying
x + -0.1666666667 = -7.361687609

Reorder the terms:
-0.1666666667 + x = -7.361687609

Solving
-0.1666666667 + x = -7.361687609

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -7.361687609 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -7.361687609 + 0.1666666667
x = -7.361687609 + 0.1666666667

Combine like terms: -7.361687609 + 0.1666666667 = -7.1950209423
x = -7.1950209423

Simplifying
x = -7.1950209423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.5283542757, -7.1950209423}

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