2x^2+6x-391=0

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Solution for 2x^2+6x-391=0 equation: 


Simplifying
2x2 + 6x + -391 = 0

Reorder the terms:
-391 + 6x + 2x2 = 0

Solving
-391 + 6x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-195.5 + 3x + x2 = 0

Move the constant term to the right:

Add '195.5' to each side of the equation.
-195.5 + 3x + 195.5 + x2 = 0 + 195.5

Reorder the terms:
-195.5 + 195.5 + 3x + x2 = 0 + 195.5

Combine like terms: -195.5 + 195.5 = 0.0
0.0 + 3x + x2 = 0 + 195.5
3x + x2 = 0 + 195.5

Combine like terms: 0 + 195.5 = 195.5
3x + x2 = 195.5

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 = 195.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 195.5 + 2.25

Combine like terms: 195.5 + 2.25 = 197.75
2.25 + 3x + x2 = 197.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 197.75

Calculate the square root of the right side: 14.06236111

Break this problem into two subproblems by setting 
(x + 1.5) equal to 14.06236111 and -14.06236111.


Subproblem 1
x + 1.5 = 14.06236111

Simplifying
x + 1.5 = 14.06236111

Reorder the terms:
1.5 + x = 14.06236111

Solving
1.5 + x = 14.06236111

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 = 14.06236111 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 14.06236111 + -1.5
x = 14.06236111 + -1.5

Combine like terms: 14.06236111 + -1.5 = 12.56236111
x = 12.56236111

Simplifying
x = 12.56236111


Subproblem 2
x + 1.5 = -14.06236111

Simplifying
x + 1.5 = -14.06236111

Reorder the terms:
1.5 + x = -14.06236111

Solving
1.5 + x = -14.06236111

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 = -14.06236111 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -14.06236111 + -1.5
x = -14.06236111 + -1.5

Combine like terms: -14.06236111 + -1.5 = -15.56236111
x = -15.56236111

Simplifying
x = -15.56236111


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.56236111, -15.56236111}

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