3x^2+14x=191

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Solution for 3x^2+14x=191 equation: 


Simplifying
3x2 + 14x = 191

Reorder the terms:
14x + 3x2 = 191

Solving
14x + 3x2 = 191

Solving for variable 'x'.

Reorder the terms:
-191 + 14x + 3x2 = 191 + -191

Combine like terms: 191 + -191 = 0
-191 + 14x + 3x2 = 0

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

Divide each side by '3'.
-63.66666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '63.66666667' to each side of the equation.
-63.66666667 + 4.666666667x + 63.66666667 + x2 = 0 + 63.66666667

Reorder the terms:
-63.66666667 + 63.66666667 + 4.666666667x + x2 = 0 + 63.66666667

Combine like terms: -63.66666667 + 63.66666667 = 0.00000000
0.00000000 + 4.666666667x + x2 = 0 + 63.66666667
4.666666667x + x2 = 0 + 63.66666667

Combine like terms: 0 + 63.66666667 = 63.66666667
4.666666667x + x2 = 63.66666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 63.66666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 63.66666667 + 5.444444448

Combine like terms: 63.66666667 + 5.444444448 = 69.111111118
5.444444448 + 4.666666667x + x2 = 69.111111118

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 69.111111118

Calculate the square root of the right side: 8.313309276

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 8.313309276 and -8.313309276.


Subproblem 1
x + 2.333333334 = 8.313309276

Simplifying
x + 2.333333334 = 8.313309276

Reorder the terms:
2.333333334 + x = 8.313309276

Solving
2.333333334 + x = 8.313309276

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 8.313309276 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 8.313309276 + -2.333333334
x = 8.313309276 + -2.333333334

Combine like terms: 8.313309276 + -2.333333334 = 5.979975942
x = 5.979975942

Simplifying
x = 5.979975942


Subproblem 2
x + 2.333333334 = -8.313309276

Simplifying
x + 2.333333334 = -8.313309276

Reorder the terms:
2.333333334 + x = -8.313309276

Solving
2.333333334 + x = -8.313309276

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -8.313309276 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -8.313309276 + -2.333333334
x = -8.313309276 + -2.333333334

Combine like terms: -8.313309276 + -2.333333334 = -10.64664261
x = -10.64664261

Simplifying
x = -10.64664261


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.979975942, -10.64664261}

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