30x^2+30x-20000=0

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Solution for 30x^2+30x-20000=0 equation: 


Simplifying
30x2 + 30x + -20000 = 0

Reorder the terms:
-20000 + 30x + 30x2 = 0

Solving
-20000 + 30x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-2000 + 3x + 3x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-2000 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2000 + 3x + 3x2 = 0

Solving
-2000 + 3x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-666.6666667 + x + x2 = 0

Move the constant term to the right:

Add '666.6666667' to each side of the equation.
-666.6666667 + x + 666.6666667 + x2 = 0 + 666.6666667

Reorder the terms:
-666.6666667 + 666.6666667 + x + x2 = 0 + 666.6666667

Combine like terms: -666.6666667 + 666.6666667 = 0.0000000
0.0000000 + x + x2 = 0 + 666.6666667
x + x2 = 0 + 666.6666667

Combine like terms: 0 + 666.6666667 = 666.6666667
x + x2 = 666.6666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 666.6666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 666.6666667 + 0.25

Combine like terms: 666.6666667 + 0.25 = 666.9166667
1.25 + x2 = 666.9166667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 666.9166667

Calculate the square root of the right side: 25.824729751

Break this problem into two subproblems by setting 
(x + 0.5) equal to 25.824729751 and -25.824729751.


Subproblem 1
x + 0.5 = 25.824729751

Simplifying
x + 0.5 = 25.824729751

Reorder the terms:
0.5 + x = 25.824729751

Solving
0.5 + x = 25.824729751

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 25.824729751 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 25.824729751 + -0.5
x = 25.824729751 + -0.5

Combine like terms: 25.824729751 + -0.5 = 25.324729751
x = 25.324729751

Simplifying
x = 25.324729751


Subproblem 2
x + 0.5 = -25.824729751

Simplifying
x + 0.5 = -25.824729751

Reorder the terms:
0.5 + x = -25.824729751

Solving
0.5 + x = -25.824729751

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -25.824729751 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -25.824729751 + -0.5
x = -25.824729751 + -0.5

Combine like terms: -25.824729751 + -0.5 = -26.324729751
x = -26.324729751

Simplifying
x = -26.324729751


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.324729751, -26.324729751}
Solution
x = {25.324729751, -26.324729751}

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