3x^2-16x-3=0

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Solution for 3x^2-16x-3=0 equation: 


Simplifying
3x2 + -16x + -3 = 0

Reorder the terms:
-3 + -16x + 3x2 = 0

Solving
-3 + -16x + 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 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -5.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5.333333333x + x2 = 0 + 1
-5.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5.333333333x + x2 = 1

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 1 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 1 + 7.111111113

Combine like terms: 1 + 7.111111113 = 8.111111113
7.111111113 + -5.333333333x + x2 = 8.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 8.111111113

Calculate the square root of the right side: 2.848001249

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 2.848001249 and -2.848001249.


Subproblem 1
x + -2.666666667 = 2.848001249

Simplifying
x + -2.666666667 = 2.848001249

Reorder the terms:
-2.666666667 + x = 2.848001249

Solving
-2.666666667 + x = 2.848001249

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 2.848001249 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 2.848001249 + 2.666666667
x = 2.848001249 + 2.666666667

Combine like terms: 2.848001249 + 2.666666667 = 5.514667916
x = 5.514667916

Simplifying
x = 5.514667916


Subproblem 2
x + -2.666666667 = -2.848001249

Simplifying
x + -2.666666667 = -2.848001249

Reorder the terms:
-2.666666667 + x = -2.848001249

Solving
-2.666666667 + x = -2.848001249

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -2.848001249 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -2.848001249 + 2.666666667
x = -2.848001249 + 2.666666667

Combine like terms: -2.848001249 + 2.666666667 = -0.181334582
x = -0.181334582

Simplifying
x = -0.181334582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.514667916, -0.181334582}

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