3x^2-28x+63=0

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Solution for 3x^2-28x+63=0 equation: 


Simplifying
3x2 + -28x + 63 = 0

Reorder the terms:
63 + -28x + 3x2 = 0

Solving
63 + -28x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
21 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -9.333333333x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -9.333333333x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -9.333333333x + x2 = 0 + -21
-9.333333333x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-9.333333333x + x2 = -21

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -21 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -21 + 21.77777778

Combine like terms: -21 + 21.77777778 = 0.77777778
21.77777778 + -9.333333333x + x2 = 0.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 0.881917105 and -0.881917105.


Subproblem 1
x + -4.666666667 = 0.881917105

Simplifying
x + -4.666666667 = 0.881917105

Reorder the terms:
-4.666666667 + x = 0.881917105

Solving
-4.666666667 + x = 0.881917105

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 0.881917105 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 0.881917105 + 4.666666667
x = 0.881917105 + 4.666666667

Combine like terms: 0.881917105 + 4.666666667 = 5.548583772
x = 5.548583772

Simplifying
x = 5.548583772


Subproblem 2
x + -4.666666667 = -0.881917105

Simplifying
x + -4.666666667 = -0.881917105

Reorder the terms:
-4.666666667 + x = -0.881917105

Solving
-4.666666667 + x = -0.881917105

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -0.881917105 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -0.881917105 + 4.666666667
x = -0.881917105 + 4.666666667

Combine like terms: -0.881917105 + 4.666666667 = 3.784749562
x = 3.784749562

Simplifying
x = 3.784749562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.548583772, 3.784749562}

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