3x^2-57x+27=0

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Solution for 3x^2-57x+27=0 equation: 


Simplifying
3x2 + -57x + 27 = 0

Reorder the terms:
27 + -57x + 3x2 = 0

Solving
27 + -57x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -19x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + -19x + x2)' equal to zero and attempt to solve:

Simplifying
9 + -19x + x2 = 0

Solving
9 + -19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -19x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -19x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -19x + x2 = 0 + -9
-19x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-19x + x2 = -9

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -9 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -9 + 90.25

Combine like terms: -9 + 90.25 = 81.25
90.25 + -19x + x2 = 81.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + -9.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
x + -9.5 = 9.013878189

Simplifying
x + -9.5 = 9.013878189

Reorder the terms:
-9.5 + x = 9.013878189

Solving
-9.5 + x = 9.013878189

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 9.013878189 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 9.013878189 + 9.5
x = 9.013878189 + 9.5

Combine like terms: 9.013878189 + 9.5 = 18.513878189
x = 18.513878189

Simplifying
x = 18.513878189


Subproblem 2
x + -9.5 = -9.013878189

Simplifying
x + -9.5 = -9.013878189

Reorder the terms:
-9.5 + x = -9.013878189

Solving
-9.5 + x = -9.013878189

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -9.013878189 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -9.013878189 + 9.5
x = -9.013878189 + 9.5

Combine like terms: -9.013878189 + 9.5 = 0.486121811
x = 0.486121811

Simplifying
x = 0.486121811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.513878189, 0.486121811}
Solution
x = {18.513878189, 0.486121811}

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