3x^2-.5x-56.5=0

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Solution for 3x^2-.5x-56.5=0 equation: 


Simplifying
3x2 + -0.5x + -56.5 = 0

Reorder the terms:
-56.5 + -0.5x + 3x2 = 0

Solving
-56.5 + -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'.
-18.83333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '18.83333333' to each side of the equation.
-18.83333333 + -0.1666666667x + 18.83333333 + x2 = 0 + 18.83333333

Reorder the terms:
-18.83333333 + 18.83333333 + -0.1666666667x + x2 = 0 + 18.83333333

Combine like terms: -18.83333333 + 18.83333333 = 0.00000000
0.00000000 + -0.1666666667x + x2 = 0 + 18.83333333
-0.1666666667x + x2 = 0 + 18.83333333

Combine like terms: 0 + 18.83333333 = 18.83333333
-0.1666666667x + x2 = 18.83333333

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 = 18.83333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 18.83333333 + 0.006944444447

Combine like terms: 18.83333333 + 0.006944444447 = 18.840277774447
0.006944444447 + -0.1666666667x + x2 = 18.840277774447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 18.840277774447

Calculate the square root of the right side: 4.340538881

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 4.340538881 and -4.340538881.


Subproblem 1
x + -0.08333333335 = 4.340538881

Simplifying
x + -0.08333333335 = 4.340538881

Reorder the terms:
-0.08333333335 + x = 4.340538881

Solving
-0.08333333335 + x = 4.340538881

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 = 4.340538881 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 4.340538881 + 0.08333333335
x = 4.340538881 + 0.08333333335

Combine like terms: 4.340538881 + 0.08333333335 = 4.42387221435
x = 4.42387221435

Simplifying
x = 4.42387221435


Subproblem 2
x + -0.08333333335 = -4.340538881

Simplifying
x + -0.08333333335 = -4.340538881

Reorder the terms:
-0.08333333335 + x = -4.340538881

Solving
-0.08333333335 + x = -4.340538881

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 = -4.340538881 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -4.340538881 + 0.08333333335
x = -4.340538881 + 0.08333333335

Combine like terms: -4.340538881 + 0.08333333335 = -4.25720554765
x = -4.25720554765

Simplifying
x = -4.25720554765


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.42387221435, -4.25720554765}

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