3x^2-8x-107=0

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Solution for 3x^2-8x-107=0 equation: 


Simplifying
3x2 + -8x + -107 = 0

Reorder the terms:
-107 + -8x + 3x2 = 0

Solving
-107 + -8x + 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'.
-35.66666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '35.66666667' to each side of the equation.
-35.66666667 + -2.666666667x + 35.66666667 + x2 = 0 + 35.66666667

Reorder the terms:
-35.66666667 + 35.66666667 + -2.666666667x + x2 = 0 + 35.66666667

Combine like terms: -35.66666667 + 35.66666667 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 35.66666667
-2.666666667x + x2 = 0 + 35.66666667

Combine like terms: 0 + 35.66666667 = 35.66666667
-2.666666667x + x2 = 35.66666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 35.66666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 35.66666667 + 1.777777780

Combine like terms: 35.66666667 + 1.777777780 = 37.44444445
1.777777780 + -2.666666667x + x2 = 37.44444445

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 37.44444445

Calculate the square root of the right side: 6.119186584

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 6.119186584 and -6.119186584.


Subproblem 1
x + -1.333333334 = 6.119186584

Simplifying
x + -1.333333334 = 6.119186584

Reorder the terms:
-1.333333334 + x = 6.119186584

Solving
-1.333333334 + x = 6.119186584

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 6.119186584 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 6.119186584 + 1.333333334
x = 6.119186584 + 1.333333334

Combine like terms: 6.119186584 + 1.333333334 = 7.452519918
x = 7.452519918

Simplifying
x = 7.452519918


Subproblem 2
x + -1.333333334 = -6.119186584

Simplifying
x + -1.333333334 = -6.119186584

Reorder the terms:
-1.333333334 + x = -6.119186584

Solving
-1.333333334 + x = -6.119186584

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -6.119186584 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -6.119186584 + 1.333333334
x = -6.119186584 + 1.333333334

Combine like terms: -6.119186584 + 1.333333334 = -4.78585325
x = -4.78585325

Simplifying
x = -4.78585325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.452519918, -4.78585325}

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