3x^2+11x-500=0

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Solution for 3x^2+11x-500=0 equation: 


Simplifying
3x2 + 11x + -500 = 0

Reorder the terms:
-500 + 11x + 3x2 = 0

Solving
-500 + 11x + 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'.
-166.6666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '166.6666667' to each side of the equation.
-166.6666667 + 3.666666667x + 166.6666667 + x2 = 0 + 166.6666667

Reorder the terms:
-166.6666667 + 166.6666667 + 3.666666667x + x2 = 0 + 166.6666667

Combine like terms: -166.6666667 + 166.6666667 = 0.0000000
0.0000000 + 3.666666667x + x2 = 0 + 166.6666667
3.666666667x + x2 = 0 + 166.6666667

Combine like terms: 0 + 166.6666667 = 166.6666667
3.666666667x + x2 = 166.6666667

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 166.6666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 166.6666667 + 3.361111114

Combine like terms: 166.6666667 + 3.361111114 = 170.027777814
3.361111114 + 3.666666667x + x2 = 170.027777814

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 170.027777814

Calculate the square root of the right side: 13.039469997

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 13.039469997 and -13.039469997.


Subproblem 1
x + 1.833333334 = 13.039469997

Simplifying
x + 1.833333334 = 13.039469997

Reorder the terms:
1.833333334 + x = 13.039469997

Solving
1.833333334 + x = 13.039469997

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 13.039469997 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 13.039469997 + -1.833333334
x = 13.039469997 + -1.833333334

Combine like terms: 13.039469997 + -1.833333334 = 11.206136663
x = 11.206136663

Simplifying
x = 11.206136663


Subproblem 2
x + 1.833333334 = -13.039469997

Simplifying
x + 1.833333334 = -13.039469997

Reorder the terms:
1.833333334 + x = -13.039469997

Solving
1.833333334 + x = -13.039469997

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -13.039469997 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -13.039469997 + -1.833333334
x = -13.039469997 + -1.833333334

Combine like terms: -13.039469997 + -1.833333334 = -14.872803331
x = -14.872803331

Simplifying
x = -14.872803331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.206136663, -14.872803331}

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