3x^2+2x-440=0

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Solution for 3x^2+2x-440=0 equation: 


Simplifying
3x2 + 2x + -440 = 0

Reorder the terms:
-440 + 2x + 3x2 = 0

Solving
-440 + 2x + 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'.
-146.6666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '146.6666667' to each side of the equation.
-146.6666667 + 0.6666666667x + 146.6666667 + x2 = 0 + 146.6666667

Reorder the terms:
-146.6666667 + 146.6666667 + 0.6666666667x + x2 = 0 + 146.6666667

Combine like terms: -146.6666667 + 146.6666667 = 0.0000000
0.0000000 + 0.6666666667x + x2 = 0 + 146.6666667
0.6666666667x + x2 = 0 + 146.6666667

Combine like terms: 0 + 146.6666667 = 146.6666667
0.6666666667x + x2 = 146.6666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 146.6666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 146.6666667 + 0.1111111112

Combine like terms: 146.6666667 + 0.1111111112 = 146.7777778112
0.1111111112 + 0.6666666667x + x2 = 146.7777778112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 146.7777778112

Calculate the square root of the right side: 12.115187898

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 12.115187898 and -12.115187898.


Subproblem 1
x + 0.3333333334 = 12.115187898

Simplifying
x + 0.3333333334 = 12.115187898

Reorder the terms:
0.3333333334 + x = 12.115187898

Solving
0.3333333334 + x = 12.115187898

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 12.115187898 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 12.115187898 + -0.3333333334
x = 12.115187898 + -0.3333333334

Combine like terms: 12.115187898 + -0.3333333334 = 11.7818545646
x = 11.7818545646

Simplifying
x = 11.7818545646


Subproblem 2
x + 0.3333333334 = -12.115187898

Simplifying
x + 0.3333333334 = -12.115187898

Reorder the terms:
0.3333333334 + x = -12.115187898

Solving
0.3333333334 + x = -12.115187898

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -12.115187898 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -12.115187898 + -0.3333333334
x = -12.115187898 + -0.3333333334

Combine like terms: -12.115187898 + -0.3333333334 = -12.4485212314
x = -12.4485212314

Simplifying
x = -12.4485212314


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.7818545646, -12.4485212314}

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