6x^2+11x-14=0

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Solution for 6x^2+11x-14=0 equation: 


Simplifying
6x2 + 11x + -14 = 0

Reorder the terms:
-14 + 11x + 6x2 = 0

Solving
-14 + 11x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-2.333333333 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 1.833333333x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 1.833333333x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 1.833333333x + x2 = 0 + 2.333333333
1.833333333x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
1.833333333x + x2 = 2.333333333

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 2.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 2.333333333 + 0.8402777775

Combine like terms: 2.333333333 + 0.8402777775 = 3.1736111105
0.8402777775 + 1.833333333x + x2 = 3.1736111105

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 3.1736111105

Calculate the square root of the right side: 1.781463194

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 1.781463194 and -1.781463194.


Subproblem 1
x + 0.9166666665 = 1.781463194

Simplifying
x + 0.9166666665 = 1.781463194

Reorder the terms:
0.9166666665 + x = 1.781463194

Solving
0.9166666665 + x = 1.781463194

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 1.781463194 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 1.781463194 + -0.9166666665
x = 1.781463194 + -0.9166666665

Combine like terms: 1.781463194 + -0.9166666665 = 0.8647965275
x = 0.8647965275

Simplifying
x = 0.8647965275


Subproblem 2
x + 0.9166666665 = -1.781463194

Simplifying
x + 0.9166666665 = -1.781463194

Reorder the terms:
0.9166666665 + x = -1.781463194

Solving
0.9166666665 + x = -1.781463194

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -1.781463194 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -1.781463194 + -0.9166666665
x = -1.781463194 + -0.9166666665

Combine like terms: -1.781463194 + -0.9166666665 = -2.6981298605
x = -2.6981298605

Simplifying
x = -2.6981298605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8647965275, -2.6981298605}

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