3x^2-3x-950=0

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Solution for 3x^2-3x-950=0 equation: 


Simplifying
3x2 + -3x + -950 = 0

Reorder the terms:
-950 + -3x + 3x2 = 0

Solving
-950 + -3x + 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'.
-316.6666667 + -1x + x2 = 0

Move the constant term to the right:

Add '316.6666667' to each side of the equation.
-316.6666667 + -1x + 316.6666667 + x2 = 0 + 316.6666667

Reorder the terms:
-316.6666667 + 316.6666667 + -1x + x2 = 0 + 316.6666667

Combine like terms: -316.6666667 + 316.6666667 = 0.0000000
0.0000000 + -1x + x2 = 0 + 316.6666667
-1x + x2 = 0 + 316.6666667

Combine like terms: 0 + 316.6666667 = 316.6666667
-1x + x2 = 316.6666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 316.6666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 316.6666667 + 0.25

Combine like terms: 316.6666667 + 0.25 = 316.9166667
0.25 + -1x + x2 = 316.9166667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 316.9166667

Calculate the square root of the right side: 17.802153429

Break this problem into two subproblems by setting 
(x + -0.5) equal to 17.802153429 and -17.802153429.


Subproblem 1
x + -0.5 = 17.802153429

Simplifying
x + -0.5 = 17.802153429

Reorder the terms:
-0.5 + x = 17.802153429

Solving
-0.5 + x = 17.802153429

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 17.802153429 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 17.802153429 + 0.5
x = 17.802153429 + 0.5

Combine like terms: 17.802153429 + 0.5 = 18.302153429
x = 18.302153429

Simplifying
x = 18.302153429


Subproblem 2
x + -0.5 = -17.802153429

Simplifying
x + -0.5 = -17.802153429

Reorder the terms:
-0.5 + x = -17.802153429

Solving
-0.5 + x = -17.802153429

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -17.802153429 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -17.802153429 + 0.5
x = -17.802153429 + 0.5

Combine like terms: -17.802153429 + 0.5 = -17.302153429
x = -17.302153429

Simplifying
x = -17.302153429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.302153429, -17.302153429}

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