9x^2-36x-14=0

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Solution for 9x^2-36x-14=0 equation: 


Simplifying
9x2 + -36x + -14 = 0

Reorder the terms:
-14 + -36x + 9x2 = 0

Solving
-14 + -36x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.555555556 + -4x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + -4x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + -4x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + -4x + x2 = 0 + 1.555555556
-4x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
-4x + x2 = 1.555555556

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.555555556 + 4

Reorder the terms:
4 + -4x + x2 = 1.555555556 + 4

Combine like terms: 1.555555556 + 4 = 5.555555556
4 + -4x + x2 = 5.555555556

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.555555556

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(x + -2) equal to 2.357022604 and -2.357022604.


Subproblem 1
x + -2 = 2.357022604

Simplifying
x + -2 = 2.357022604

Reorder the terms:
-2 + x = 2.357022604

Solving
-2 + x = 2.357022604

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.357022604 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.357022604 + 2
x = 2.357022604 + 2

Combine like terms: 2.357022604 + 2 = 4.357022604
x = 4.357022604

Simplifying
x = 4.357022604


Subproblem 2
x + -2 = -2.357022604

Simplifying
x + -2 = -2.357022604

Reorder the terms:
-2 + x = -2.357022604

Solving
-2 + x = -2.357022604

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.357022604 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.357022604 + 2
x = -2.357022604 + 2

Combine like terms: -2.357022604 + 2 = -0.357022604
x = -0.357022604

Simplifying
x = -0.357022604


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.357022604, -0.357022604}

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