3x^2-49x+84=0

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Solution for 3x^2-49x+84=0 equation: 


Simplifying
3x2 + -49x + 84 = 0

Reorder the terms:
84 + -49x + 3x2 = 0

Solving
84 + -49x + 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'.
28 + -16.33333333x + x2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -16.33333333x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -16.33333333x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -16.33333333x + x2 = 0 + -28
-16.33333333x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-16.33333333x + x2 = -28

The x term is -16.33333333x.  Take half its coefficient (-8.166666665).
Square it (66.69444442) and add it to both sides.

Add '66.69444442' to each side of the equation.
-16.33333333x + 66.69444442 + x2 = -28 + 66.69444442

Reorder the terms:
66.69444442 + -16.33333333x + x2 = -28 + 66.69444442

Combine like terms: -28 + 66.69444442 = 38.69444442
66.69444442 + -16.33333333x + x2 = 38.69444442

Factor a perfect square on the left side:
(x + -8.166666665)(x + -8.166666665) = 38.69444442

Calculate the square root of the right side: 6.220485867

Break this problem into two subproblems by setting 
(x + -8.166666665) equal to 6.220485867 and -6.220485867.


Subproblem 1
x + -8.166666665 = 6.220485867

Simplifying
x + -8.166666665 = 6.220485867

Reorder the terms:
-8.166666665 + x = 6.220485867

Solving
-8.166666665 + x = 6.220485867

Solving for variable 'x'.

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

Add '8.166666665' to each side of the equation.
-8.166666665 + 8.166666665 + x = 6.220485867 + 8.166666665

Combine like terms: -8.166666665 + 8.166666665 = 0.000000000
0.000000000 + x = 6.220485867 + 8.166666665
x = 6.220485867 + 8.166666665

Combine like terms: 6.220485867 + 8.166666665 = 14.387152532
x = 14.387152532

Simplifying
x = 14.387152532


Subproblem 2
x + -8.166666665 = -6.220485867

Simplifying
x + -8.166666665 = -6.220485867

Reorder the terms:
-8.166666665 + x = -6.220485867

Solving
-8.166666665 + x = -6.220485867

Solving for variable 'x'.

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

Add '8.166666665' to each side of the equation.
-8.166666665 + 8.166666665 + x = -6.220485867 + 8.166666665

Combine like terms: -8.166666665 + 8.166666665 = 0.000000000
0.000000000 + x = -6.220485867 + 8.166666665
x = -6.220485867 + 8.166666665

Combine like terms: -6.220485867 + 8.166666665 = 1.946180798
x = 1.946180798

Simplifying
x = 1.946180798


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.387152532, 1.946180798}

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