14x^2-84x-36=0

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Solution for 14x^2-84x-36=0 equation: 


Simplifying
14x2 + -84x + -36 = 0

Reorder the terms:
-36 + -84x + 14x2 = 0

Solving
-36 + -84x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -42x + 7x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + -42x + 7x2)' equal to zero and attempt to solve:

Simplifying
-18 + -42x + 7x2 = 0

Solving
-18 + -42x + 7x2 = 0

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

Divide each side by '7'.
-2.571428571 + -6x + x2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + -6x + 2.571428571 + x2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + -6x + x2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + -6x + x2 = 0 + 2.571428571
-6x + x2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
-6x + x2 = 2.571428571

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 2.571428571 + 9

Reorder the terms:
9 + -6x + x2 = 2.571428571 + 9

Combine like terms: 2.571428571 + 9 = 11.571428571
9 + -6x + x2 = 11.571428571

Factor a perfect square on the left side:
(x + -3)(x + -3) = 11.571428571

Calculate the square root of the right side: 3.401680257

Break this problem into two subproblems by setting 
(x + -3) equal to 3.401680257 and -3.401680257.


Subproblem 1
x + -3 = 3.401680257

Simplifying
x + -3 = 3.401680257

Reorder the terms:
-3 + x = 3.401680257

Solving
-3 + x = 3.401680257

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.401680257 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.401680257 + 3
x = 3.401680257 + 3

Combine like terms: 3.401680257 + 3 = 6.401680257
x = 6.401680257

Simplifying
x = 6.401680257


Subproblem 2
x + -3 = -3.401680257

Simplifying
x + -3 = -3.401680257

Reorder the terms:
-3 + x = -3.401680257

Solving
-3 + x = -3.401680257

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.401680257 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.401680257 + 3
x = -3.401680257 + 3

Combine like terms: -3.401680257 + 3 = -0.401680257
x = -0.401680257

Simplifying
x = -0.401680257


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.401680257, -0.401680257}
Solution
x = {6.401680257, -0.401680257}

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