3x^2-18x-88=0

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Solution for 3x^2-18x-88=0 equation: 


Simplifying
3x2 + -18x + -88 = 0

Reorder the terms:
-88 + -18x + 3x2 = 0

Solving
-88 + -18x + 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'.
-29.33333333 + -6x + x2 = 0

Move the constant term to the right:

Add '29.33333333' to each side of the equation.
-29.33333333 + -6x + 29.33333333 + x2 = 0 + 29.33333333

Reorder the terms:
-29.33333333 + 29.33333333 + -6x + x2 = 0 + 29.33333333

Combine like terms: -29.33333333 + 29.33333333 = 0.00000000
0.00000000 + -6x + x2 = 0 + 29.33333333
-6x + x2 = 0 + 29.33333333

Combine like terms: 0 + 29.33333333 = 29.33333333
-6x + x2 = 29.33333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 29.33333333 + 9

Reorder the terms:
9 + -6x + x2 = 29.33333333 + 9

Combine like terms: 29.33333333 + 9 = 38.33333333
9 + -6x + x2 = 38.33333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 38.33333333

Calculate the square root of the right side: 6.191391873

Break this problem into two subproblems by setting 
(x + -3) equal to 6.191391873 and -6.191391873.


Subproblem 1
x + -3 = 6.191391873

Simplifying
x + -3 = 6.191391873

Reorder the terms:
-3 + x = 6.191391873

Solving
-3 + x = 6.191391873

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.191391873 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.191391873 + 3
x = 6.191391873 + 3

Combine like terms: 6.191391873 + 3 = 9.191391873
x = 9.191391873

Simplifying
x = 9.191391873


Subproblem 2
x + -3 = -6.191391873

Simplifying
x + -3 = -6.191391873

Reorder the terms:
-3 + x = -6.191391873

Solving
-3 + x = -6.191391873

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.191391873 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.191391873 + 3
x = -6.191391873 + 3

Combine like terms: -6.191391873 + 3 = -3.191391873
x = -3.191391873

Simplifying
x = -3.191391873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.191391873, -3.191391873}

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