3x^2+43x-110=0

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Solution for 3x^2+43x-110=0 equation: 


Simplifying
3x2 + 43x + -110 = 0

Reorder the terms:
-110 + 43x + 3x2 = 0

Solving
-110 + 43x + 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'.
-36.66666667 + 14.33333333x + x2 = 0

Move the constant term to the right:

Add '36.66666667' to each side of the equation.
-36.66666667 + 14.33333333x + 36.66666667 + x2 = 0 + 36.66666667

Reorder the terms:
-36.66666667 + 36.66666667 + 14.33333333x + x2 = 0 + 36.66666667

Combine like terms: -36.66666667 + 36.66666667 = 0.00000000
0.00000000 + 14.33333333x + x2 = 0 + 36.66666667
14.33333333x + x2 = 0 + 36.66666667

Combine like terms: 0 + 36.66666667 = 36.66666667
14.33333333x + x2 = 36.66666667

The x term is 14.33333333x.  Take half its coefficient (7.166666665).
Square it (51.36111109) and add it to both sides.

Add '51.36111109' to each side of the equation.
14.33333333x + 51.36111109 + x2 = 36.66666667 + 51.36111109

Reorder the terms:
51.36111109 + 14.33333333x + x2 = 36.66666667 + 51.36111109

Combine like terms: 36.66666667 + 51.36111109 = 88.02777776
51.36111109 + 14.33333333x + x2 = 88.02777776

Factor a perfect square on the left side:
(x + 7.166666665)(x + 7.166666665) = 88.02777776

Calculate the square root of the right side: 9.382311962

Break this problem into two subproblems by setting 
(x + 7.166666665) equal to 9.382311962 and -9.382311962.


Subproblem 1
x + 7.166666665 = 9.382311962

Simplifying
x + 7.166666665 = 9.382311962

Reorder the terms:
7.166666665 + x = 9.382311962

Solving
7.166666665 + x = 9.382311962

Solving for variable 'x'.

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

Add '-7.166666665' to each side of the equation.
7.166666665 + -7.166666665 + x = 9.382311962 + -7.166666665

Combine like terms: 7.166666665 + -7.166666665 = 0.000000000
0.000000000 + x = 9.382311962 + -7.166666665
x = 9.382311962 + -7.166666665

Combine like terms: 9.382311962 + -7.166666665 = 2.215645297
x = 2.215645297

Simplifying
x = 2.215645297


Subproblem 2
x + 7.166666665 = -9.382311962

Simplifying
x + 7.166666665 = -9.382311962

Reorder the terms:
7.166666665 + x = -9.382311962

Solving
7.166666665 + x = -9.382311962

Solving for variable 'x'.

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

Add '-7.166666665' to each side of the equation.
7.166666665 + -7.166666665 + x = -9.382311962 + -7.166666665

Combine like terms: 7.166666665 + -7.166666665 = 0.000000000
0.000000000 + x = -9.382311962 + -7.166666665
x = -9.382311962 + -7.166666665

Combine like terms: -9.382311962 + -7.166666665 = -16.548978627
x = -16.548978627

Simplifying
x = -16.548978627


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.215645297, -16.548978627}

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