3x^2+19x-5.5=0

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Solution for 3x^2+19x-5.5=0 equation: 


Simplifying
3x2 + 19x + -5.5 = 0

Reorder the terms:
-5.5 + 19x + 3x2 = 0

Solving
-5.5 + 19x + 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'.
-1.833333333 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 6.333333333x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 6.333333333x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 6.333333333x + x2 = 0 + 1.833333333
6.333333333x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
6.333333333x + x2 = 1.833333333

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 1.833333333 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 1.833333333 + 10.02777778

Combine like terms: 1.833333333 + 10.02777778 = 11.861111113
10.02777778 + 6.333333333x + x2 = 11.861111113

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 11.861111113

Calculate the square root of the right side: 3.443996387

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 3.443996387 and -3.443996387.


Subproblem 1
x + 3.166666667 = 3.443996387

Simplifying
x + 3.166666667 = 3.443996387

Reorder the terms:
3.166666667 + x = 3.443996387

Solving
3.166666667 + x = 3.443996387

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 3.443996387 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 3.443996387 + -3.166666667
x = 3.443996387 + -3.166666667

Combine like terms: 3.443996387 + -3.166666667 = 0.27732972
x = 0.27732972

Simplifying
x = 0.27732972


Subproblem 2
x + 3.166666667 = -3.443996387

Simplifying
x + 3.166666667 = -3.443996387

Reorder the terms:
3.166666667 + x = -3.443996387

Solving
3.166666667 + x = -3.443996387

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -3.443996387 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -3.443996387 + -3.166666667
x = -3.443996387 + -3.166666667

Combine like terms: -3.443996387 + -3.166666667 = -6.610663054
x = -6.610663054

Simplifying
x = -6.610663054


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.27732972, -6.610663054}

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