3x^2+35x-6.5=0

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Solution for 3x^2+35x-6.5=0 equation: 


Simplifying
3x2 + 35x + -6.5 = 0

Reorder the terms:
-6.5 + 35x + 3x2 = 0

Solving
-6.5 + 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'.
-2.166666667 + 11.66666667x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 11.66666667x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 11.66666667x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 11.66666667x + x2 = 0 + 2.166666667
11.66666667x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
11.66666667x + x2 = 2.166666667

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 = 2.166666667 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667x + x2 = 2.166666667 + 34.02777780

Combine like terms: 2.166666667 + 34.02777780 = 36.194444467
34.02777780 + 11.66666667x + x2 = 36.194444467

Factor a perfect square on the left side:
(x + 5.833333335)(x + 5.833333335) = 36.194444467

Calculate the square root of the right side: 6.016181884

Break this problem into two subproblems by setting 
(x + 5.833333335) equal to 6.016181884 and -6.016181884.


Subproblem 1
x + 5.833333335 = 6.016181884

Simplifying
x + 5.833333335 = 6.016181884

Reorder the terms:
5.833333335 + x = 6.016181884

Solving
5.833333335 + x = 6.016181884

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 = 6.016181884 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = 6.016181884 + -5.833333335
x = 6.016181884 + -5.833333335

Combine like terms: 6.016181884 + -5.833333335 = 0.182848549
x = 0.182848549

Simplifying
x = 0.182848549


Subproblem 2
x + 5.833333335 = -6.016181884

Simplifying
x + 5.833333335 = -6.016181884

Reorder the terms:
5.833333335 + x = -6.016181884

Solving
5.833333335 + x = -6.016181884

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 = -6.016181884 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = -6.016181884 + -5.833333335
x = -6.016181884 + -5.833333335

Combine like terms: -6.016181884 + -5.833333335 = -11.849515219
x = -11.849515219

Simplifying
x = -11.849515219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.182848549, -11.849515219}

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