3x^2-27x+10=0

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Solution for 3x^2-27x+10=0 equation: 


Simplifying
3x2 + -27x + 10 = 0

Reorder the terms:
10 + -27x + 3x2 = 0

Solving
10 + -27x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3.333333333 + -9x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -9x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -9x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -9x + x2 = 0 + -3.333333333
-9x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-9x + x2 = -3.333333333

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -3.333333333 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -3.333333333 + 20.25

Combine like terms: -3.333333333 + 20.25 = 16.916666667
20.25 + -9x + x2 = 16.916666667

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 16.916666667

Calculate the square root of the right side: 4.11298756

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.11298756 and -4.11298756.


Subproblem 1
x + -4.5 = 4.11298756

Simplifying
x + -4.5 = 4.11298756

Reorder the terms:
-4.5 + x = 4.11298756

Solving
-4.5 + x = 4.11298756

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.11298756 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.11298756 + 4.5
x = 4.11298756 + 4.5

Combine like terms: 4.11298756 + 4.5 = 8.61298756
x = 8.61298756

Simplifying
x = 8.61298756


Subproblem 2
x + -4.5 = -4.11298756

Simplifying
x + -4.5 = -4.11298756

Reorder the terms:
-4.5 + x = -4.11298756

Solving
-4.5 + x = -4.11298756

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.11298756 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.11298756 + 4.5
x = -4.11298756 + 4.5

Combine like terms: -4.11298756 + 4.5 = 0.38701244
x = 0.38701244

Simplifying
x = 0.38701244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.61298756, 0.38701244}

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