3x^2-0.5x-80.5=0

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Solution for 3x^2-0.5x-80.5=0 equation: 


Simplifying
3x2 + -0.5x + -80.5 = 0

Reorder the terms:
-80.5 + -0.5x + 3x2 = 0

Solving
-80.5 + -0.5x + 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'.
-26.83333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '26.83333333' to each side of the equation.
-26.83333333 + -0.1666666667x + 26.83333333 + x2 = 0 + 26.83333333

Reorder the terms:
-26.83333333 + 26.83333333 + -0.1666666667x + x2 = 0 + 26.83333333

Combine like terms: -26.83333333 + 26.83333333 = 0.00000000
0.00000000 + -0.1666666667x + x2 = 0 + 26.83333333
-0.1666666667x + x2 = 0 + 26.83333333

Combine like terms: 0 + 26.83333333 = 26.83333333
-0.1666666667x + x2 = 26.83333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 26.83333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 26.83333333 + 0.006944444447

Combine like terms: 26.83333333 + 0.006944444447 = 26.840277774447
0.006944444447 + -0.1666666667x + x2 = 26.840277774447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 26.840277774447

Calculate the square root of the right side: 5.180760347

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 5.180760347 and -5.180760347.


Subproblem 1
x + -0.08333333335 = 5.180760347

Simplifying
x + -0.08333333335 = 5.180760347

Reorder the terms:
-0.08333333335 + x = 5.180760347

Solving
-0.08333333335 + x = 5.180760347

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 5.180760347 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 5.180760347 + 0.08333333335
x = 5.180760347 + 0.08333333335

Combine like terms: 5.180760347 + 0.08333333335 = 5.26409368035
x = 5.26409368035

Simplifying
x = 5.26409368035


Subproblem 2
x + -0.08333333335 = -5.180760347

Simplifying
x + -0.08333333335 = -5.180760347

Reorder the terms:
-0.08333333335 + x = -5.180760347

Solving
-0.08333333335 + x = -5.180760347

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -5.180760347 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -5.180760347 + 0.08333333335
x = -5.180760347 + 0.08333333335

Combine like terms: -5.180760347 + 0.08333333335 = -5.09742701365
x = -5.09742701365

Simplifying
x = -5.09742701365


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.26409368035, -5.09742701365}

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