3x^2-95x-35=0

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Solution for 3x^2-95x-35=0 equation: 


Simplifying
3x2 + -95x + -35 = 0

Reorder the terms:
-35 + -95x + 3x2 = 0

Solving
-35 + -95x + 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'.
-11.66666667 + -31.66666667x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + -31.66666667x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + -31.66666667x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + -31.66666667x + x2 = 0 + 11.66666667
-31.66666667x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
-31.66666667x + x2 = 11.66666667

The x term is -31.66666667x.  Take half its coefficient (-15.83333334).
Square it (250.6944447) and add it to both sides.

Add '250.6944447' to each side of the equation.
-31.66666667x + 250.6944447 + x2 = 11.66666667 + 250.6944447

Reorder the terms:
250.6944447 + -31.66666667x + x2 = 11.66666667 + 250.6944447

Combine like terms: 11.66666667 + 250.6944447 = 262.36111137
250.6944447 + -31.66666667x + x2 = 262.36111137

Factor a perfect square on the left side:
(x + -15.83333334)(x + -15.83333334) = 262.36111137

Calculate the square root of the right side: 16.197564983

Break this problem into two subproblems by setting 
(x + -15.83333334) equal to 16.197564983 and -16.197564983.


Subproblem 1
x + -15.83333334 = 16.197564983

Simplifying
x + -15.83333334 = 16.197564983

Reorder the terms:
-15.83333334 + x = 16.197564983

Solving
-15.83333334 + x = 16.197564983

Solving for variable 'x'.

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

Add '15.83333334' to each side of the equation.
-15.83333334 + 15.83333334 + x = 16.197564983 + 15.83333334

Combine like terms: -15.83333334 + 15.83333334 = 0.00000000
0.00000000 + x = 16.197564983 + 15.83333334
x = 16.197564983 + 15.83333334

Combine like terms: 16.197564983 + 15.83333334 = 32.030898323
x = 32.030898323

Simplifying
x = 32.030898323


Subproblem 2
x + -15.83333334 = -16.197564983

Simplifying
x + -15.83333334 = -16.197564983

Reorder the terms:
-15.83333334 + x = -16.197564983

Solving
-15.83333334 + x = -16.197564983

Solving for variable 'x'.

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

Add '15.83333334' to each side of the equation.
-15.83333334 + 15.83333334 + x = -16.197564983 + 15.83333334

Combine like terms: -15.83333334 + 15.83333334 = 0.00000000
0.00000000 + x = -16.197564983 + 15.83333334
x = -16.197564983 + 15.83333334

Combine like terms: -16.197564983 + 15.83333334 = -0.364231643
x = -0.364231643

Simplifying
x = -0.364231643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.030898323, -0.364231643}

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