3x^2+38x+50=0

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Solution for 3x^2+38x+50=0 equation: 


Simplifying
3x2 + 38x + 50 = 0

Reorder the terms:
50 + 38x + 3x2 = 0

Solving
50 + 38x + 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'.
16.66666667 + 12.66666667x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + 12.66666667x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + 12.66666667x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + 12.66666667x + x2 = 0 + -16.66666667
12.66666667x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
12.66666667x + x2 = -16.66666667

The x term is 12.66666667x.  Take half its coefficient (6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
12.66666667x + 40.11111113 + x2 = -16.66666667 + 40.11111113

Reorder the terms:
40.11111113 + 12.66666667x + x2 = -16.66666667 + 40.11111113

Combine like terms: -16.66666667 + 40.11111113 = 23.44444446
40.11111113 + 12.66666667x + x2 = 23.44444446

Factor a perfect square on the left side:
(x + 6.333333335)(x + 6.333333335) = 23.44444446

Calculate the square root of the right side: 4.84194635

Break this problem into two subproblems by setting 
(x + 6.333333335) equal to 4.84194635 and -4.84194635.


Subproblem 1
x + 6.333333335 = 4.84194635

Simplifying
x + 6.333333335 = 4.84194635

Reorder the terms:
6.333333335 + x = 4.84194635

Solving
6.333333335 + x = 4.84194635

Solving for variable 'x'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + x = 4.84194635 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + x = 4.84194635 + -6.333333335
x = 4.84194635 + -6.333333335

Combine like terms: 4.84194635 + -6.333333335 = -1.491386985
x = -1.491386985

Simplifying
x = -1.491386985


Subproblem 2
x + 6.333333335 = -4.84194635

Simplifying
x + 6.333333335 = -4.84194635

Reorder the terms:
6.333333335 + x = -4.84194635

Solving
6.333333335 + x = -4.84194635

Solving for variable 'x'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + x = -4.84194635 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + x = -4.84194635 + -6.333333335
x = -4.84194635 + -6.333333335

Combine like terms: -4.84194635 + -6.333333335 = -11.175279685
x = -11.175279685

Simplifying
x = -11.175279685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.491386985, -11.175279685}

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