3x^2-0.5x-4.75=0

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Solution for 3x^2-0.5x-4.75=0 equation: 


Simplifying
3x2 + -0.5x + -4.75 = 0

Reorder the terms:
-4.75 + -0.5x + 3x2 = 0

Solving
-4.75 + -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'.
-1.583333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.583333333' to each side of the equation.
-1.583333333 + -0.1666666667x + 1.583333333 + x2 = 0 + 1.583333333

Reorder the terms:
-1.583333333 + 1.583333333 + -0.1666666667x + x2 = 0 + 1.583333333

Combine like terms: -1.583333333 + 1.583333333 = 0.000000000
0.000000000 + -0.1666666667x + x2 = 0 + 1.583333333
-0.1666666667x + x2 = 0 + 1.583333333

Combine like terms: 0 + 1.583333333 = 1.583333333
-0.1666666667x + x2 = 1.583333333

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 = 1.583333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 1.583333333 + 0.006944444447

Combine like terms: 1.583333333 + 0.006944444447 = 1.590277777447
0.006944444447 + -0.1666666667x + x2 = 1.590277777447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 1.590277777447

Calculate the square root of the right side: 1.261062162

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 1.261062162 and -1.261062162.


Subproblem 1
x + -0.08333333335 = 1.261062162

Simplifying
x + -0.08333333335 = 1.261062162

Reorder the terms:
-0.08333333335 + x = 1.261062162

Solving
-0.08333333335 + x = 1.261062162

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 = 1.261062162 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 1.261062162 + 0.08333333335
x = 1.261062162 + 0.08333333335

Combine like terms: 1.261062162 + 0.08333333335 = 1.34439549535
x = 1.34439549535

Simplifying
x = 1.34439549535


Subproblem 2
x + -0.08333333335 = -1.261062162

Simplifying
x + -0.08333333335 = -1.261062162

Reorder the terms:
-0.08333333335 + x = -1.261062162

Solving
-0.08333333335 + x = -1.261062162

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 = -1.261062162 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -1.261062162 + 0.08333333335
x = -1.261062162 + 0.08333333335

Combine like terms: -1.261062162 + 0.08333333335 = -1.17772882865
x = -1.17772882865

Simplifying
x = -1.17772882865


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.34439549535, -1.17772882865}

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