x^2+3x=36000

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Solution for x^2+3x=36000 equation: 


Simplifying
x2 + 3x = 36000

Reorder the terms:
3x + x2 = 36000

Solving
3x + x2 = 36000

Solving for variable 'x'.

Reorder the terms:
-36000 + 3x + x2 = 36000 + -36000

Combine like terms: 36000 + -36000 = 0
-36000 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36000' to each side of the equation.
-36000 + 3x + 36000 + x2 = 0 + 36000

Reorder the terms:
-36000 + 36000 + 3x + x2 = 0 + 36000

Combine like terms: -36000 + 36000 = 0
0 + 3x + x2 = 0 + 36000
3x + x2 = 0 + 36000

Combine like terms: 0 + 36000 = 36000
3x + x2 = 36000

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 36000 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 36000 + 2.25

Combine like terms: 36000 + 2.25 = 36002.25
2.25 + 3x + x2 = 36002.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 36002.25

Calculate the square root of the right side: 189.742588788

Break this problem into two subproblems by setting 
(x + 1.5) equal to 189.742588788 and -189.742588788.


Subproblem 1
x + 1.5 = 189.742588788

Simplifying
x + 1.5 = 189.742588788

Reorder the terms:
1.5 + x = 189.742588788

Solving
1.5 + x = 189.742588788

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 189.742588788 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 189.742588788 + -1.5
x = 189.742588788 + -1.5

Combine like terms: 189.742588788 + -1.5 = 188.242588788
x = 188.242588788

Simplifying
x = 188.242588788


Subproblem 2
x + 1.5 = -189.742588788

Simplifying
x + 1.5 = -189.742588788

Reorder the terms:
1.5 + x = -189.742588788

Solving
1.5 + x = -189.742588788

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -189.742588788 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -189.742588788 + -1.5
x = -189.742588788 + -1.5

Combine like terms: -189.742588788 + -1.5 = -191.242588788
x = -191.242588788

Simplifying
x = -191.242588788


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {188.242588788, -191.242588788}

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