3x^2+35x+14=0

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Solution for 3x^2+35x+14=0 equation: 


Simplifying
3x2 + 35x + 14 = 0

Reorder the terms:
14 + 35x + 3x2 = 0

Solving
14 + 35x + 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'.
4.666666667 + 11.66666667x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 11.66666667x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 11.66666667x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 11.66666667x + x2 = 0 + -4.666666667
11.66666667x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
11.66666667x + x2 = -4.666666667

The x term is 11.66666667x.  Take half its coefficient (5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
11.66666667x + 34.02777780 + x2 = -4.666666667 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667x + x2 = -4.666666667 + 34.02777780

Combine like terms: -4.666666667 + 34.02777780 = 29.361111133
34.02777780 + 11.66666667x + x2 = 29.361111133

Factor a perfect square on the left side:
(x + 5.833333335)(x + 5.833333335) = 29.361111133

Calculate the square root of the right side: 5.418589404

Break this problem into two subproblems by setting 
(x + 5.833333335) equal to 5.418589404 and -5.418589404.


Subproblem 1
x + 5.833333335 = 5.418589404

Simplifying
x + 5.833333335 = 5.418589404

Reorder the terms:
5.833333335 + x = 5.418589404

Solving
5.833333335 + x = 5.418589404

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = 5.418589404 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = 5.418589404 + -5.833333335
x = 5.418589404 + -5.833333335

Combine like terms: 5.418589404 + -5.833333335 = -0.414743931
x = -0.414743931

Simplifying
x = -0.414743931


Subproblem 2
x + 5.833333335 = -5.418589404

Simplifying
x + 5.833333335 = -5.418589404

Reorder the terms:
5.833333335 + x = -5.418589404

Solving
5.833333335 + x = -5.418589404

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = -5.418589404 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = -5.418589404 + -5.833333335
x = -5.418589404 + -5.833333335

Combine like terms: -5.418589404 + -5.833333335 = -11.251922739
x = -11.251922739

Simplifying
x = -11.251922739


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.414743931, -11.251922739}

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