9x^2-39x+16=0

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Solution for 9x^2-39x+16=0 equation: 


Simplifying
9x2 + -39x + 16 = 0

Reorder the terms:
16 + -39x + 9x2 = 0

Solving
16 + -39x + 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'.
1.777777778 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + -4.333333333x + -1.777777778 + x2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + -4.333333333x + x2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + -1.777777778
-4.333333333x + x2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
-4.333333333x + x2 = -1.777777778

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -1.777777778 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -1.777777778 + 4.694444446

Combine like terms: -1.777777778 + 4.694444446 = 2.916666668
4.694444446 + -4.333333333x + x2 = 2.916666668

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 2.916666668

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 1.707825128 and -1.707825128.


Subproblem 1
x + -2.166666667 = 1.707825128

Simplifying
x + -2.166666667 = 1.707825128

Reorder the terms:
-2.166666667 + x = 1.707825128

Solving
-2.166666667 + x = 1.707825128

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 1.707825128 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 1.707825128 + 2.166666667
x = 1.707825128 + 2.166666667

Combine like terms: 1.707825128 + 2.166666667 = 3.874491795
x = 3.874491795

Simplifying
x = 3.874491795


Subproblem 2
x + -2.166666667 = -1.707825128

Simplifying
x + -2.166666667 = -1.707825128

Reorder the terms:
-2.166666667 + x = -1.707825128

Solving
-2.166666667 + x = -1.707825128

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -1.707825128 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -1.707825128 + 2.166666667
x = -1.707825128 + 2.166666667

Combine like terms: -1.707825128 + 2.166666667 = 0.458841539
x = 0.458841539

Simplifying
x = 0.458841539


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.874491795, 0.458841539}

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