3x^2-14x-5=5

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Solution for 3x^2-14x-5=5 equation: 


Simplifying
3x2 + -14x + -5 = 5

Reorder the terms:
-5 + -14x + 3x2 = 5

Solving
-5 + -14x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -5 + -14x + 3x2 = 5 + -5

Combine like terms: -5 + -5 = -10
-10 + -14x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-10 + -14x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -4.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -4.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 3.333333333
-4.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-4.666666667x + x2 = 3.333333333

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 = 3.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 3.333333333 + 5.444444448

Combine like terms: 3.333333333 + 5.444444448 = 8.777777781
5.444444448 + -4.666666667x + x2 = 8.777777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 8.777777781

Calculate the square root of the right side: 2.962731473

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.962731473 and -2.962731473.


Subproblem 1
x + -2.333333334 = 2.962731473

Simplifying
x + -2.333333334 = 2.962731473

Reorder the terms:
-2.333333334 + x = 2.962731473

Solving
-2.333333334 + x = 2.962731473

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 = 2.962731473 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.962731473 + 2.333333334
x = 2.962731473 + 2.333333334

Combine like terms: 2.962731473 + 2.333333334 = 5.296064807
x = 5.296064807

Simplifying
x = 5.296064807


Subproblem 2
x + -2.333333334 = -2.962731473

Simplifying
x + -2.333333334 = -2.962731473

Reorder the terms:
-2.333333334 + x = -2.962731473

Solving
-2.333333334 + x = -2.962731473

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 = -2.962731473 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.962731473 + 2.333333334
x = -2.962731473 + 2.333333334

Combine like terms: -2.962731473 + 2.333333334 = -0.629398139
x = -0.629398139

Simplifying
x = -0.629398139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.296064807, -0.629398139}

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