3x^2-77x-20=0

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Solution for 3x^2-77x-20=0 equation: 


Simplifying
3x2 + -77x + -20 = 0

Reorder the terms:
-20 + -77x + 3x2 = 0

Solving
-20 + -77x + 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'.
-6.666666667 + -25.66666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -25.66666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -25.66666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -25.66666667x + x2 = 0 + 6.666666667
-25.66666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-25.66666667x + x2 = 6.666666667

The x term is -25.66666667x.  Take half its coefficient (-12.83333334).
Square it (164.6944446) and add it to both sides.

Add '164.6944446' to each side of the equation.
-25.66666667x + 164.6944446 + x2 = 6.666666667 + 164.6944446

Reorder the terms:
164.6944446 + -25.66666667x + x2 = 6.666666667 + 164.6944446

Combine like terms: 6.666666667 + 164.6944446 = 171.361111267
164.6944446 + -25.66666667x + x2 = 171.361111267

Factor a perfect square on the left side:
(x + -12.83333334)(x + -12.83333334) = 171.361111267

Calculate the square root of the right side: 13.090496983

Break this problem into two subproblems by setting 
(x + -12.83333334) equal to 13.090496983 and -13.090496983.


Subproblem 1
x + -12.83333334 = 13.090496983

Simplifying
x + -12.83333334 = 13.090496983

Reorder the terms:
-12.83333334 + x = 13.090496983

Solving
-12.83333334 + x = 13.090496983

Solving for variable 'x'.

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

Add '12.83333334' to each side of the equation.
-12.83333334 + 12.83333334 + x = 13.090496983 + 12.83333334

Combine like terms: -12.83333334 + 12.83333334 = 0.00000000
0.00000000 + x = 13.090496983 + 12.83333334
x = 13.090496983 + 12.83333334

Combine like terms: 13.090496983 + 12.83333334 = 25.923830323
x = 25.923830323

Simplifying
x = 25.923830323


Subproblem 2
x + -12.83333334 = -13.090496983

Simplifying
x + -12.83333334 = -13.090496983

Reorder the terms:
-12.83333334 + x = -13.090496983

Solving
-12.83333334 + x = -13.090496983

Solving for variable 'x'.

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

Add '12.83333334' to each side of the equation.
-12.83333334 + 12.83333334 + x = -13.090496983 + 12.83333334

Combine like terms: -12.83333334 + 12.83333334 = 0.00000000
0.00000000 + x = -13.090496983 + 12.83333334
x = -13.090496983 + 12.83333334

Combine like terms: -13.090496983 + 12.83333334 = -0.257163643
x = -0.257163643

Simplifying
x = -0.257163643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.923830323, -0.257163643}

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