9x^2-57x+20=0

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Solution for 9x^2-57x+20=0 equation: 


Simplifying
9x2 + -57x + 20 = 0

Reorder the terms:
20 + -57x + 9x2 = 0

Solving
20 + -57x + 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'.
2.222222222 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + -6.333333333x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + -6.333333333x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + -6.333333333x + x2 = 0 + -2.222222222
-6.333333333x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
-6.333333333x + x2 = -2.222222222

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = -2.222222222 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = -2.222222222 + 10.02777778

Combine like terms: -2.222222222 + 10.02777778 = 7.805555558
10.02777778 + -6.333333333x + x2 = 7.805555558

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 7.805555558

Calculate the square root of the right side: 2.793842436

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 2.793842436 and -2.793842436.


Subproblem 1
x + -3.166666667 = 2.793842436

Simplifying
x + -3.166666667 = 2.793842436

Reorder the terms:
-3.166666667 + x = 2.793842436

Solving
-3.166666667 + x = 2.793842436

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = 2.793842436 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = 2.793842436 + 3.166666667
x = 2.793842436 + 3.166666667

Combine like terms: 2.793842436 + 3.166666667 = 5.960509103
x = 5.960509103

Simplifying
x = 5.960509103


Subproblem 2
x + -3.166666667 = -2.793842436

Simplifying
x + -3.166666667 = -2.793842436

Reorder the terms:
-3.166666667 + x = -2.793842436

Solving
-3.166666667 + x = -2.793842436

Solving for variable 'x'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + x = -2.793842436 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + x = -2.793842436 + 3.166666667
x = -2.793842436 + 3.166666667

Combine like terms: -2.793842436 + 3.166666667 = 0.372824231
x = 0.372824231

Simplifying
x = 0.372824231


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.960509103, 0.372824231}

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