4x^2+36x-2000=0

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Solution for 4x^2+36x-2000=0 equation: 


Simplifying
4x2 + 36x + -2000 = 0

Reorder the terms:
-2000 + 36x + 4x2 = 0

Solving
-2000 + 36x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-500 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-500 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-500 + 9x + x2 = 0

Solving
-500 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 9x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 9x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 9x + x2 = 0 + 500
9x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
9x + x2 = 500

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 500 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 500 + 20.25

Combine like terms: 500 + 20.25 = 520.25
20.25 + 9x + x2 = 520.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 520.25

Calculate the square root of the right side: 22.808989456

Break this problem into two subproblems by setting 
(x + 4.5) equal to 22.808989456 and -22.808989456.


Subproblem 1
x + 4.5 = 22.808989456

Simplifying
x + 4.5 = 22.808989456

Reorder the terms:
4.5 + x = 22.808989456

Solving
4.5 + x = 22.808989456

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 22.808989456 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 22.808989456 + -4.5
x = 22.808989456 + -4.5

Combine like terms: 22.808989456 + -4.5 = 18.308989456
x = 18.308989456

Simplifying
x = 18.308989456


Subproblem 2
x + 4.5 = -22.808989456

Simplifying
x + 4.5 = -22.808989456

Reorder the terms:
4.5 + x = -22.808989456

Solving
4.5 + x = -22.808989456

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -22.808989456 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -22.808989456 + -4.5
x = -22.808989456 + -4.5

Combine like terms: -22.808989456 + -4.5 = -27.308989456
x = -27.308989456

Simplifying
x = -27.308989456


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.308989456, -27.308989456}
Solution
x = {18.308989456, -27.308989456}

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