6x^2-40x-55=0

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Solution for 6x^2-40x-55=0 equation: 


Simplifying
6x2 + -40x + -55 = 0

Reorder the terms:
-55 + -40x + 6x2 = 0

Solving
-55 + -40x + 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'.
-9.166666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '9.166666667' to each side of the equation.
-9.166666667 + -6.666666667x + 9.166666667 + x2 = 0 + 9.166666667

Reorder the terms:
-9.166666667 + 9.166666667 + -6.666666667x + x2 = 0 + 9.166666667

Combine like terms: -9.166666667 + 9.166666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + 9.166666667
-6.666666667x + x2 = 0 + 9.166666667

Combine like terms: 0 + 9.166666667 = 9.166666667
-6.666666667x + x2 = 9.166666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 9.166666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 9.166666667 + 11.11111112

Combine like terms: 9.166666667 + 11.11111112 = 20.277777787
11.11111112 + -6.666666667x + x2 = 20.277777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 20.277777787

Calculate the square root of the right side: 4.503085363

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 4.503085363 and -4.503085363.


Subproblem 1
x + -3.333333334 = 4.503085363

Simplifying
x + -3.333333334 = 4.503085363

Reorder the terms:
-3.333333334 + x = 4.503085363

Solving
-3.333333334 + x = 4.503085363

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 4.503085363 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 4.503085363 + 3.333333334
x = 4.503085363 + 3.333333334

Combine like terms: 4.503085363 + 3.333333334 = 7.836418697
x = 7.836418697

Simplifying
x = 7.836418697


Subproblem 2
x + -3.333333334 = -4.503085363

Simplifying
x + -3.333333334 = -4.503085363

Reorder the terms:
-3.333333334 + x = -4.503085363

Solving
-3.333333334 + x = -4.503085363

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -4.503085363 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -4.503085363 + 3.333333334
x = -4.503085363 + 3.333333334

Combine like terms: -4.503085363 + 3.333333334 = -1.169752029
x = -1.169752029

Simplifying
x = -1.169752029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.836418697, -1.169752029}

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