3x^2-37x+48=0

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Solution for 3x^2-37x+48=0 equation: 


Simplifying
3x2 + -37x + 48 = 0

Reorder the terms:
48 + -37x + 3x2 = 0

Solving
48 + -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'.
16 + -12.33333333x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12.33333333x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -12.33333333x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12.33333333x + x2 = 0 + -16
-12.33333333x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-12.33333333x + x2 = -16

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 = -16 + 38.02777776

Reorder the terms:
38.02777776 + -12.33333333x + x2 = -16 + 38.02777776

Combine like terms: -16 + 38.02777776 = 22.02777776
38.02777776 + -12.33333333x + x2 = 22.02777776

Factor a perfect square on the left side:
(x + -6.166666665)(x + -6.166666665) = 22.02777776

Calculate the square root of the right side: 4.693375945

Break this problem into two subproblems by setting 
(x + -6.166666665) equal to 4.693375945 and -4.693375945.


Subproblem 1
x + -6.166666665 = 4.693375945

Simplifying
x + -6.166666665 = 4.693375945

Reorder the terms:
-6.166666665 + x = 4.693375945

Solving
-6.166666665 + x = 4.693375945

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 = 4.693375945 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = 4.693375945 + 6.166666665
x = 4.693375945 + 6.166666665

Combine like terms: 4.693375945 + 6.166666665 = 10.86004261
x = 10.86004261

Simplifying
x = 10.86004261


Subproblem 2
x + -6.166666665 = -4.693375945

Simplifying
x + -6.166666665 = -4.693375945

Reorder the terms:
-6.166666665 + x = -4.693375945

Solving
-6.166666665 + x = -4.693375945

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 = -4.693375945 + 6.166666665

Combine like terms: -6.166666665 + 6.166666665 = 0.000000000
0.000000000 + x = -4.693375945 + 6.166666665
x = -4.693375945 + 6.166666665

Combine like terms: -4.693375945 + 6.166666665 = 1.47329072
x = 1.47329072

Simplifying
x = 1.47329072


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.86004261, 1.47329072}

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