3x^2-14x-36=0

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Solution for 3x^2-14x-36=0 equation: 


Simplifying
3x2 + -14x + -36 = 0

Reorder the terms:
-36 + -14x + 3x2 = 0

Solving
-36 + -14x + 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'.
-12 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -4.666666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -4.666666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -4.666666667x + x2 = 0 + 12
-4.666666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-4.666666667x + x2 = 12

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 = 12 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 12 + 5.444444448

Combine like terms: 12 + 5.444444448 = 17.444444448
5.444444448 + -4.666666667x + x2 = 17.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 17.444444448

Calculate the square root of the right side: 4.176654696

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 4.176654696 and -4.176654696.


Subproblem 1
x + -2.333333334 = 4.176654696

Simplifying
x + -2.333333334 = 4.176654696

Reorder the terms:
-2.333333334 + x = 4.176654696

Solving
-2.333333334 + x = 4.176654696

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 = 4.176654696 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 4.176654696 + 2.333333334
x = 4.176654696 + 2.333333334

Combine like terms: 4.176654696 + 2.333333334 = 6.50998803
x = 6.50998803

Simplifying
x = 6.50998803


Subproblem 2
x + -2.333333334 = -4.176654696

Simplifying
x + -2.333333334 = -4.176654696

Reorder the terms:
-2.333333334 + x = -4.176654696

Solving
-2.333333334 + x = -4.176654696

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 = -4.176654696 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -4.176654696 + 2.333333334
x = -4.176654696 + 2.333333334

Combine like terms: -4.176654696 + 2.333333334 = -1.843321362
x = -1.843321362

Simplifying
x = -1.843321362


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.50998803, -1.843321362}

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