3x^2-15x+9=0

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Solution for 3x^2-15x+9=0 equation: 


Simplifying
3x2 + -15x + 9 = 0

Reorder the terms:
9 + -15x + 3x2 = 0

Solving
9 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -5x + x2 = 0

Solving
3 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x + x2 = 0 + -3
-5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5x + x2 = -3

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5x + x2 = 3.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + -2.5 = 1.802775638

Simplifying
x + -2.5 = 1.802775638

Reorder the terms:
-2.5 + x = 1.802775638

Solving
-2.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.802775638 + 2.5
x = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
x = 4.302775638

Simplifying
x = 4.302775638


Subproblem 2
x + -2.5 = -1.802775638

Simplifying
x + -2.5 = -1.802775638

Reorder the terms:
-2.5 + x = -1.802775638

Solving
-2.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.802775638 + 2.5
x = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
x = 0.697224362

Simplifying
x = 0.697224362


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.302775638, 0.697224362}
Solution
x = {4.302775638, 0.697224362}

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