3x^2-23x-5.5=0

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Solution for 3x^2-23x-5.5=0 equation: 


Simplifying
3x2 + -23x + -5.5 = 0

Reorder the terms:
-5.5 + -23x + 3x2 = 0

Solving
-5.5 + -23x + 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'.
-1.833333333 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -7.666666667x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -7.666666667x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -7.666666667x + x2 = 0 + 1.833333333
-7.666666667x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-7.666666667x + x2 = 1.833333333

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = 1.833333333 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = 1.833333333 + 14.69444445

Combine like terms: 1.833333333 + 14.69444445 = 16.527777783
14.69444445 + -7.666666667x + x2 = 16.527777783

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 16.527777783

Calculate the square root of the right side: 4.065436973

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 4.065436973 and -4.065436973.


Subproblem 1
x + -3.833333334 = 4.065436973

Simplifying
x + -3.833333334 = 4.065436973

Reorder the terms:
-3.833333334 + x = 4.065436973

Solving
-3.833333334 + x = 4.065436973

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = 4.065436973 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = 4.065436973 + 3.833333334
x = 4.065436973 + 3.833333334

Combine like terms: 4.065436973 + 3.833333334 = 7.898770307
x = 7.898770307

Simplifying
x = 7.898770307


Subproblem 2
x + -3.833333334 = -4.065436973

Simplifying
x + -3.833333334 = -4.065436973

Reorder the terms:
-3.833333334 + x = -4.065436973

Solving
-3.833333334 + x = -4.065436973

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = -4.065436973 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = -4.065436973 + 3.833333334
x = -4.065436973 + 3.833333334

Combine like terms: -4.065436973 + 3.833333334 = -0.232103639
x = -0.232103639

Simplifying
x = -0.232103639


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.898770307, -0.232103639}

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