3x^2-63x+63=0

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Solution for 3x^2-63x+63=0 equation: 


Simplifying
3x2 + -63x + 63 = 0

Reorder the terms:
63 + -63x + 3x2 = 0

Solving
63 + -63x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -21x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(21 + -21x + x2)' equal to zero and attempt to solve:

Simplifying
21 + -21x + x2 = 0

Solving
21 + -21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -21x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -21x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -21x + x2 = 0 + -21
-21x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-21x + x2 = -21

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -21 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -21 + 110.25

Combine like terms: -21 + 110.25 = 89.25
110.25 + -21x + x2 = 89.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 89.25

Calculate the square root of the right side: 9.447221814

Break this problem into two subproblems by setting 
(x + -10.5) equal to 9.447221814 and -9.447221814.


Subproblem 1
x + -10.5 = 9.447221814

Simplifying
x + -10.5 = 9.447221814

Reorder the terms:
-10.5 + x = 9.447221814

Solving
-10.5 + x = 9.447221814

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 9.447221814 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 9.447221814 + 10.5
x = 9.447221814 + 10.5

Combine like terms: 9.447221814 + 10.5 = 19.947221814
x = 19.947221814

Simplifying
x = 19.947221814


Subproblem 2
x + -10.5 = -9.447221814

Simplifying
x + -10.5 = -9.447221814

Reorder the terms:
-10.5 + x = -9.447221814

Solving
-10.5 + x = -9.447221814

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -9.447221814 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -9.447221814 + 10.5
x = -9.447221814 + 10.5

Combine like terms: -9.447221814 + 10.5 = 1.052778186
x = 1.052778186

Simplifying
x = 1.052778186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.947221814, 1.052778186}
Solution
x = {19.947221814, 1.052778186}

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