3x^2+5x-55=0

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Solution for 3x^2+5x-55=0 equation: 


Simplifying
3x2 + 5x + -55 = 0

Reorder the terms:
-55 + 5x + 3x2 = 0

Solving
-55 + 5x + 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'.
-18.33333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '18.33333333' to each side of the equation.
-18.33333333 + 1.666666667x + 18.33333333 + x2 = 0 + 18.33333333

Reorder the terms:
-18.33333333 + 18.33333333 + 1.666666667x + x2 = 0 + 18.33333333

Combine like terms: -18.33333333 + 18.33333333 = 0.00000000
0.00000000 + 1.666666667x + x2 = 0 + 18.33333333
1.666666667x + x2 = 0 + 18.33333333

Combine like terms: 0 + 18.33333333 = 18.33333333
1.666666667x + x2 = 18.33333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 18.33333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 18.33333333 + 0.6944444447

Combine like terms: 18.33333333 + 0.6944444447 = 19.0277777747
0.6944444447 + 1.666666667x + x2 = 19.0277777747

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 19.0277777747

Calculate the square root of the right side: 4.362084109

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 4.362084109 and -4.362084109.


Subproblem 1
x + 0.8333333335 = 4.362084109

Simplifying
x + 0.8333333335 = 4.362084109

Reorder the terms:
0.8333333335 + x = 4.362084109

Solving
0.8333333335 + x = 4.362084109

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 4.362084109 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 4.362084109 + -0.8333333335
x = 4.362084109 + -0.8333333335

Combine like terms: 4.362084109 + -0.8333333335 = 3.5287507755
x = 3.5287507755

Simplifying
x = 3.5287507755


Subproblem 2
x + 0.8333333335 = -4.362084109

Simplifying
x + 0.8333333335 = -4.362084109

Reorder the terms:
0.8333333335 + x = -4.362084109

Solving
0.8333333335 + x = -4.362084109

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -4.362084109 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -4.362084109 + -0.8333333335
x = -4.362084109 + -0.8333333335

Combine like terms: -4.362084109 + -0.8333333335 = -5.1954174425
x = -5.1954174425

Simplifying
x = -5.1954174425


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5287507755, -5.1954174425}

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