3x^2+35x-44=0

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Solution for 3x^2+35x-44=0 equation: 


Simplifying
3x2 + 35x + -44 = 0

Reorder the terms:
-44 + 35x + 3x2 = 0

Solving
-44 + 35x + 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'.
-14.66666667 + 11.66666667x + x2 = 0

Move the constant term to the right:

Add '14.66666667' to each side of the equation.
-14.66666667 + 11.66666667x + 14.66666667 + x2 = 0 + 14.66666667

Reorder the terms:
-14.66666667 + 14.66666667 + 11.66666667x + x2 = 0 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + 11.66666667x + x2 = 0 + 14.66666667
11.66666667x + x2 = 0 + 14.66666667

Combine like terms: 0 + 14.66666667 = 14.66666667
11.66666667x + x2 = 14.66666667

The x term is 11.66666667x.  Take half its coefficient (5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
11.66666667x + 34.02777780 + x2 = 14.66666667 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667x + x2 = 14.66666667 + 34.02777780

Combine like terms: 14.66666667 + 34.02777780 = 48.69444447
34.02777780 + 11.66666667x + x2 = 48.69444447

Factor a perfect square on the left side:
(x + 5.833333335)(x + 5.833333335) = 48.69444447

Calculate the square root of the right side: 6.978140474

Break this problem into two subproblems by setting 
(x + 5.833333335) equal to 6.978140474 and -6.978140474.


Subproblem 1
x + 5.833333335 = 6.978140474

Simplifying
x + 5.833333335 = 6.978140474

Reorder the terms:
5.833333335 + x = 6.978140474

Solving
5.833333335 + x = 6.978140474

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = 6.978140474 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = 6.978140474 + -5.833333335
x = 6.978140474 + -5.833333335

Combine like terms: 6.978140474 + -5.833333335 = 1.144807139
x = 1.144807139

Simplifying
x = 1.144807139


Subproblem 2
x + 5.833333335 = -6.978140474

Simplifying
x + 5.833333335 = -6.978140474

Reorder the terms:
5.833333335 + x = -6.978140474

Solving
5.833333335 + x = -6.978140474

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = -6.978140474 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = -6.978140474 + -5.833333335
x = -6.978140474 + -5.833333335

Combine like terms: -6.978140474 + -5.833333335 = -12.811473809
x = -12.811473809

Simplifying
x = -12.811473809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.144807139, -12.811473809}

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