3x^2-45x+45=0

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Solution for 3x^2-45x+45=0 equation: 


Simplifying
3x2 + -45x + 45 = 0

Reorder the terms:
45 + -45x + 3x2 = 0

Solving
45 + -45x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -15x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(15 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
15 + -15x + x2 = 0

Solving
15 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -15x + -15 + x2 = 0 + -15

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

Combine like terms: 15 + -15 = 0
0 + -15x + x2 = 0 + -15
-15x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-15x + x2 = -15

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -15 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -15 + 56.25

Combine like terms: -15 + 56.25 = 41.25
56.25 + -15x + x2 = 41.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + -7.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + -7.5 = 6.422616289

Simplifying
x + -7.5 = 6.422616289

Reorder the terms:
-7.5 + x = 6.422616289

Solving
-7.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 6.422616289 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 6.422616289 + 7.5
x = 6.422616289 + 7.5

Combine like terms: 6.422616289 + 7.5 = 13.922616289
x = 13.922616289

Simplifying
x = 13.922616289


Subproblem 2
x + -7.5 = -6.422616289

Simplifying
x + -7.5 = -6.422616289

Reorder the terms:
-7.5 + x = -6.422616289

Solving
-7.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -6.422616289 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -6.422616289 + 7.5
x = -6.422616289 + 7.5

Combine like terms: -6.422616289 + 7.5 = 1.077383711
x = 1.077383711

Simplifying
x = 1.077383711


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.922616289, 1.077383711}
Solution
x = {13.922616289, 1.077383711}

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