6x^2-16x-13=0

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Solution for 6x^2-16x-13=0 equation: 


Simplifying
6x2 + -16x + -13 = 0

Reorder the terms:
-13 + -16x + 6x2 = 0

Solving
-13 + -16x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-2.166666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + -2.666666667x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + -2.666666667x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + 2.166666667
-2.666666667x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
-2.666666667x + x2 = 2.166666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 2.166666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 2.166666667 + 1.777777780

Combine like terms: 2.166666667 + 1.777777780 = 3.944444447
1.777777780 + -2.666666667x + x2 = 3.944444447

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 3.944444447

Calculate the square root of the right side: 1.986062549

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.986062549 and -1.986062549.


Subproblem 1
x + -1.333333334 = 1.986062549

Simplifying
x + -1.333333334 = 1.986062549

Reorder the terms:
-1.333333334 + x = 1.986062549

Solving
-1.333333334 + x = 1.986062549

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.986062549 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.986062549 + 1.333333334
x = 1.986062549 + 1.333333334

Combine like terms: 1.986062549 + 1.333333334 = 3.319395883
x = 3.319395883

Simplifying
x = 3.319395883


Subproblem 2
x + -1.333333334 = -1.986062549

Simplifying
x + -1.333333334 = -1.986062549

Reorder the terms:
-1.333333334 + x = -1.986062549

Solving
-1.333333334 + x = -1.986062549

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.986062549 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.986062549 + 1.333333334
x = -1.986062549 + 1.333333334

Combine like terms: -1.986062549 + 1.333333334 = -0.652729215
x = -0.652729215

Simplifying
x = -0.652729215


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.319395883, -0.652729215}

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