3x^2+14x+1=-13

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Solution for 3x^2+14x+1=-13 equation: 


Simplifying
3x2 + 14x + 1 = -13

Reorder the terms:
1 + 14x + 3x2 = -13

Solving
1 + 14x + 3x2 = -13

Solving for variable 'x'.

Reorder the terms:
1 + 13 + 14x + 3x2 = -13 + 13

Combine like terms: 1 + 13 = 14
14 + 14x + 3x2 = -13 + 13

Combine like terms: -13 + 13 = 0
14 + 14x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = -4.666666667 + 5.444444448

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

Combine like terms: -4.666666667 + 5.444444448 = 0.777777781
5.444444448 + 4.666666667x + x2 = 0.777777781

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 0.777777781

Calculate the square root of the right side: 0.881917106

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 0.881917106 and -0.881917106.


Subproblem 1
x + 2.333333334 = 0.881917106

Simplifying
x + 2.333333334 = 0.881917106

Reorder the terms:
2.333333334 + x = 0.881917106

Solving
2.333333334 + x = 0.881917106

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 = 0.881917106 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 0.881917106 + -2.333333334
x = 0.881917106 + -2.333333334

Combine like terms: 0.881917106 + -2.333333334 = -1.451416228
x = -1.451416228

Simplifying
x = -1.451416228


Subproblem 2
x + 2.333333334 = -0.881917106

Simplifying
x + 2.333333334 = -0.881917106

Reorder the terms:
2.333333334 + x = -0.881917106

Solving
2.333333334 + x = -0.881917106

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 = -0.881917106 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -0.881917106 + -2.333333334
x = -0.881917106 + -2.333333334

Combine like terms: -0.881917106 + -2.333333334 = -3.21525044
x = -3.21525044

Simplifying
x = -3.21525044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.451416228, -3.21525044}

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