9x^2-30x+10=0

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Solution for 9x^2-30x+10=0 equation: 


Simplifying
9x2 + -30x + 10 = 0

Reorder the terms:
10 + -30x + 9x2 = 0

Solving
10 + -30x + 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'.
1.111111111 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + -3.333333333x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + -3.333333333x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -1.111111111
-3.333333333x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
-3.333333333x + x2 = -1.111111111

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -1.111111111 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -1.111111111 + 2.777777779

Combine like terms: -1.111111111 + 2.777777779 = 1.666666668
2.777777779 + -3.333333333x + x2 = 1.666666668

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 1.666666668

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 1.290994449 and -1.290994449.


Subproblem 1
x + -1.666666667 = 1.290994449

Simplifying
x + -1.666666667 = 1.290994449

Reorder the terms:
-1.666666667 + x = 1.290994449

Solving
-1.666666667 + x = 1.290994449

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 1.290994449 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 1.290994449 + 1.666666667
x = 1.290994449 + 1.666666667

Combine like terms: 1.290994449 + 1.666666667 = 2.957661116
x = 2.957661116

Simplifying
x = 2.957661116


Subproblem 2
x + -1.666666667 = -1.290994449

Simplifying
x + -1.666666667 = -1.290994449

Reorder the terms:
-1.666666667 + x = -1.290994449

Solving
-1.666666667 + x = -1.290994449

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -1.290994449 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -1.290994449 + 1.666666667
x = -1.290994449 + 1.666666667

Combine like terms: -1.290994449 + 1.666666667 = 0.375672218
x = 0.375672218

Simplifying
x = 0.375672218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.957661116, 0.375672218}

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