3x^2+9x-194=0

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Solution for 3x^2+9x-194=0 equation:


Simplifying
3x2 + 9x + -194 = 0

Reorder the terms:
-194 + 9x + 3x2 = 0

Solving
-194 + 9x + 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'.
-64.66666667 + 3x + x2 = 0

Move the constant term to the right:

Add '64.66666667' to each side of the equation.
-64.66666667 + 3x + 64.66666667 + x2 = 0 + 64.66666667

Reorder the terms:
-64.66666667 + 64.66666667 + 3x + x2 = 0 + 64.66666667

Combine like terms: -64.66666667 + 64.66666667 = 0.00000000
0.00000000 + 3x + x2 = 0 + 64.66666667
3x + x2 = 0 + 64.66666667

Combine like terms: 0 + 64.66666667 = 64.66666667
3x + x2 = 64.66666667

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 64.66666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 64.66666667 + 2.25

Combine like terms: 64.66666667 + 2.25 = 66.91666667
2.25 + 3x + x2 = 66.91666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 66.91666667

Calculate the square root of the right side: 8.180260795

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.180260795 and -8.180260795.


Subproblem 1
x + 1.5 = 8.180260795

Simplifying
x + 1.5 = 8.180260795

Reorder the terms:
1.5 + x = 8.180260795

Solving
1.5 + x = 8.180260795

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 8.180260795 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.180260795 + -1.5
x = 8.180260795 + -1.5

Combine like terms: 8.180260795 + -1.5 = 6.680260795
x = 6.680260795

Simplifying
x = 6.680260795


Subproblem 2
x + 1.5 = -8.180260795

Simplifying
x + 1.5 = -8.180260795

Reorder the terms:
1.5 + x = -8.180260795

Solving
1.5 + x = -8.180260795

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -8.180260795 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.180260795 + -1.5
x = -8.180260795 + -1.5

Combine like terms: -8.180260795 + -1.5 = -9.680260795
x = -9.680260795

Simplifying
x = -9.680260795


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.680260795, -9.680260795}

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