3x^2+15x-196=0

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Solution for 3x^2+15x-196=0 equation: 


Simplifying
3x2 + 15x + -196 = 0

Reorder the terms:
-196 + 15x + 3x2 = 0

Solving
-196 + 15x + 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'.
-65.33333333 + 5x + x2 = 0

Move the constant term to the right:

Add '65.33333333' to each side of the equation.
-65.33333333 + 5x + 65.33333333 + x2 = 0 + 65.33333333

Reorder the terms:
-65.33333333 + 65.33333333 + 5x + x2 = 0 + 65.33333333

Combine like terms: -65.33333333 + 65.33333333 = 0.00000000
0.00000000 + 5x + x2 = 0 + 65.33333333
5x + x2 = 0 + 65.33333333

Combine like terms: 0 + 65.33333333 = 65.33333333
5x + x2 = 65.33333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 65.33333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 65.33333333 + 6.25

Combine like terms: 65.33333333 + 6.25 = 71.58333333
6.25 + 5x + x2 = 71.58333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 71.58333333

Calculate the square root of the right side: 8.460693431

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.460693431 and -8.460693431.


Subproblem 1
x + 2.5 = 8.460693431

Simplifying
x + 2.5 = 8.460693431

Reorder the terms:
2.5 + x = 8.460693431

Solving
2.5 + x = 8.460693431

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 8.460693431 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.460693431 + -2.5
x = 8.460693431 + -2.5

Combine like terms: 8.460693431 + -2.5 = 5.960693431
x = 5.960693431

Simplifying
x = 5.960693431


Subproblem 2
x + 2.5 = -8.460693431

Simplifying
x + 2.5 = -8.460693431

Reorder the terms:
2.5 + x = -8.460693431

Solving
2.5 + x = -8.460693431

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -8.460693431 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.460693431 + -2.5
x = -8.460693431 + -2.5

Combine like terms: -8.460693431 + -2.5 = -10.960693431
x = -10.960693431

Simplifying
x = -10.960693431


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.960693431, -10.960693431}

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