500+40x-3x^2=0

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Solution for 500+40x-3x^2=0 equation: 


Simplifying
500 + 40x + -3x2 = 0

Solving
500 + 40x + -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 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '166.6666667' to each side of the equation.
-166.6666667 + -13.33333333x + 166.6666667 + x2 = 0 + 166.6666667

Reorder the terms:
-166.6666667 + 166.6666667 + -13.33333333x + x2 = 0 + 166.6666667

Combine like terms: -166.6666667 + 166.6666667 = 0.0000000
0.0000000 + -13.33333333x + x2 = 0 + 166.6666667
-13.33333333x + x2 = 0 + 166.6666667

Combine like terms: 0 + 166.6666667 = 166.6666667
-13.33333333x + x2 = 166.6666667

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 166.6666667 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 166.6666667 + 44.44444442

Combine like terms: 166.6666667 + 44.44444442 = 211.11111112
44.44444442 + -13.33333333x + x2 = 211.11111112

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 211.11111112

Calculate the square root of the right side: 14.529663145

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 14.529663145 and -14.529663145.


Subproblem 1
x + -6.666666665 = 14.529663145

Simplifying
x + -6.666666665 = 14.529663145

Reorder the terms:
-6.666666665 + x = 14.529663145

Solving
-6.666666665 + x = 14.529663145

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 14.529663145 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 14.529663145 + 6.666666665
x = 14.529663145 + 6.666666665

Combine like terms: 14.529663145 + 6.666666665 = 21.19632981
x = 21.19632981

Simplifying
x = 21.19632981


Subproblem 2
x + -6.666666665 = -14.529663145

Simplifying
x + -6.666666665 = -14.529663145

Reorder the terms:
-6.666666665 + x = -14.529663145

Solving
-6.666666665 + x = -14.529663145

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -14.529663145 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -14.529663145 + 6.666666665
x = -14.529663145 + 6.666666665

Combine like terms: -14.529663145 + 6.666666665 = -7.86299648
x = -7.86299648

Simplifying
x = -7.86299648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.19632981, -7.86299648}

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