0.3x^2+9x-12000=0

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Solution for 0.3x^2+9x-12000=0 equation: 


Simplifying
0.3x2 + 9x + -12000 = 0

Reorder the terms:
-12000 + 9x + 0.3x2 = 0

Solving
-12000 + 9x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-40000 + 30x + x2 = 0

Move the constant term to the right:

Add '40000' to each side of the equation.
-40000 + 30x + 40000 + x2 = 0 + 40000

Reorder the terms:
-40000 + 40000 + 30x + x2 = 0 + 40000

Combine like terms: -40000 + 40000 = 0
0 + 30x + x2 = 0 + 40000
30x + x2 = 0 + 40000

Combine like terms: 0 + 40000 = 40000
30x + x2 = 40000

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 40000 + 225

Reorder the terms:
225 + 30x + x2 = 40000 + 225

Combine like terms: 40000 + 225 = 40225
225 + 30x + x2 = 40225

Factor a perfect square on the left side:
(x + 15)(x + 15) = 40225

Calculate the square root of the right side: 200.561711201

Break this problem into two subproblems by setting 
(x + 15) equal to 200.561711201 and -200.561711201.


Subproblem 1
x + 15 = 200.561711201

Simplifying
x + 15 = 200.561711201

Reorder the terms:
15 + x = 200.561711201

Solving
15 + x = 200.561711201

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 200.561711201 + -15

Combine like terms: 15 + -15 = 0
0 + x = 200.561711201 + -15
x = 200.561711201 + -15

Combine like terms: 200.561711201 + -15 = 185.561711201
x = 185.561711201

Simplifying
x = 185.561711201


Subproblem 2
x + 15 = -200.561711201

Simplifying
x + 15 = -200.561711201

Reorder the terms:
15 + x = -200.561711201

Solving
15 + x = -200.561711201

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -200.561711201 + -15

Combine like terms: 15 + -15 = 0
0 + x = -200.561711201 + -15
x = -200.561711201 + -15

Combine like terms: -200.561711201 + -15 = -215.561711201
x = -215.561711201

Simplifying
x = -215.561711201


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {185.561711201, -215.561711201}

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