3x^2-30x+9=0

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Solution for 3x^2-30x+9=0 equation: 


Simplifying
3x2 + -30x + 9 = 0

Reorder the terms:
9 + -30x + 3x2 = 0

Solving
9 + -30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -10x + x2 = 0

Solving
3 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -10x + -3 + x2 = 0 + -3

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

Combine like terms: 3 + -3 = 0
0 + -10x + x2 = 0 + -3
-10x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-10x + x2 = -3

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -3 + 25

Reorder the terms:
25 + -10x + x2 = -3 + 25

Combine like terms: -3 + 25 = 22
25 + -10x + x2 = 22

Factor a perfect square on the left side:
(x + -5)(x + -5) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -5) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + -5 = 4.69041576

Simplifying
x + -5 = 4.69041576

Reorder the terms:
-5 + x = 4.69041576

Solving
-5 + x = 4.69041576

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.69041576 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.69041576 + 5
x = 4.69041576 + 5

Combine like terms: 4.69041576 + 5 = 9.69041576
x = 9.69041576

Simplifying
x = 9.69041576


Subproblem 2
x + -5 = -4.69041576

Simplifying
x + -5 = -4.69041576

Reorder the terms:
-5 + x = -4.69041576

Solving
-5 + x = -4.69041576

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.69041576 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.69041576 + 5
x = -4.69041576 + 5

Combine like terms: -4.69041576 + 5 = 0.30958424
x = 0.30958424

Simplifying
x = 0.30958424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.69041576, 0.30958424}
Solution
x = {9.69041576, 0.30958424}

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