3x^2-37x+98=0

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Solution for 3x^2-37x+98=0 equation: 


Simplifying
3x2 + -37x + 98 = 0

Reorder the terms:
98 + -37x + 3x2 = 0

Solving
98 + -37x + 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'.
32.66666667 + -12.33333333x + x2 = 0

Move the constant term to the right:

Add '-32.66666667' to each side of the equation.
32.66666667 + -12.33333333x + -32.66666667 + x2 = 0 + -32.66666667

Reorder the terms:
32.66666667 + -32.66666667 + -12.33333333x + x2 = 0 + -32.66666667

Combine like terms: 32.66666667 + -32.66666667 = 0.00000000
0.00000000 + -12.33333333x + x2 = 0 + -32.66666667
-12.33333333x + x2 = 0 + -32.66666667

Combine like terms: 0 + -32.66666667 = -32.66666667
-12.33333333x + x2 = -32.66666667

The x term is -12.33333333x.  Take half its coefficient (-6.166666665).
Square it (38.02777776) and add it to both sides.

Add '38.02777776' to each side of the equation.
-12.33333333x + 38.02777776 + x2 = -32.66666667 + 38.02777776

Reorder the terms:
38.02777776 + -12.33333333x + x2 = -32.66666667 + 38.02777776

Combine like terms: -32.66666667 + 38.02777776 = 5.36111109
38.02777776 + -12.33333333x + x2 = 5.36111109

Factor a perfect square on the left side:
(x + -6.166666665)(x + -6.166666665) = 5.36111109

Calculate the square root of the right side: 2.315407327

Break this problem into two subproblems by setting 
(x + -6.166666665) equal to 2.315407327 and -2.315407327.


Subproblem 1
x + -6.166666665 = 2.315407327

Simplifying
x + -6.166666665 = 2.315407327

Reorder the terms:
-6.166666665 + x = 2.315407327

Solving
-6.166666665 + x = 2.315407327

Solving for variable 'x'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + x = 2.315407327 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = 2.315407327 + 6.166666665
x = 2.315407327 + 6.166666665

Combine like terms: 2.315407327 + 6.166666665 = 8.482073992
x = 8.482073992

Simplifying
x = 8.482073992


Subproblem 2
x + -6.166666665 = -2.315407327

Simplifying
x + -6.166666665 = -2.315407327

Reorder the terms:
-6.166666665 + x = -2.315407327

Solving
-6.166666665 + x = -2.315407327

Solving for variable 'x'.

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

Add '6.166666665' to each side of the equation.
-6.166666665 + 6.166666665 + x = -2.315407327 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = -2.315407327 + 6.166666665
x = -2.315407327 + 6.166666665

Combine like terms: -2.315407327 + 6.166666665 = 3.851259338
x = 3.851259338

Simplifying
x = 3.851259338


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.482073992, 3.851259338}

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