150=12x-0.025x^2

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Solution for 150=12x-0.025x^2 equation: 


Simplifying
150 = 12x + -0.025x2

Solving
150 = 12x + -0.025x2

Solving for variable 'x'.

Reorder the terms:
150 + -12x + 0.025x2 = 12x + -12x + -0.025x2 + 0.025x2

Combine like terms: 12x + -12x = 0
150 + -12x + 0.025x2 = 0 + -0.025x2 + 0.025x2
150 + -12x + 0.025x2 = -0.025x2 + 0.025x2

Combine like terms: -0.025x2 + 0.025x2 = 0.000
150 + -12x + 0.025x2 = 0.000

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

Divide each side by '0.025'.
6000 + -480x + x2 = 0

Move the constant term to the right:

Add '-6000' to each side of the equation.
6000 + -480x + -6000 + x2 = 0 + -6000

Reorder the terms:
6000 + -6000 + -480x + x2 = 0 + -6000

Combine like terms: 6000 + -6000 = 0
0 + -480x + x2 = 0 + -6000
-480x + x2 = 0 + -6000

Combine like terms: 0 + -6000 = -6000
-480x + x2 = -6000

The x term is -480x.  Take half its coefficient (-240).
Square it (57600) and add it to both sides.

Add '57600' to each side of the equation.
-480x + 57600 + x2 = -6000 + 57600

Reorder the terms:
57600 + -480x + x2 = -6000 + 57600

Combine like terms: -6000 + 57600 = 51600
57600 + -480x + x2 = 51600

Factor a perfect square on the left side:
(x + -240)(x + -240) = 51600

Calculate the square root of the right side: 227.156333832

Break this problem into two subproblems by setting 
(x + -240) equal to 227.156333832 and -227.156333832.


Subproblem 1
x + -240 = 227.156333832

Simplifying
x + -240 = 227.156333832

Reorder the terms:
-240 + x = 227.156333832

Solving
-240 + x = 227.156333832

Solving for variable 'x'.

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

Add '240' to each side of the equation.
-240 + 240 + x = 227.156333832 + 240

Combine like terms: -240 + 240 = 0
0 + x = 227.156333832 + 240
x = 227.156333832 + 240

Combine like terms: 227.156333832 + 240 = 467.156333832
x = 467.156333832

Simplifying
x = 467.156333832


Subproblem 2
x + -240 = -227.156333832

Simplifying
x + -240 = -227.156333832

Reorder the terms:
-240 + x = -227.156333832

Solving
-240 + x = -227.156333832

Solving for variable 'x'.

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

Add '240' to each side of the equation.
-240 + 240 + x = -227.156333832 + 240

Combine like terms: -240 + 240 = 0
0 + x = -227.156333832 + 240
x = -227.156333832 + 240

Combine like terms: -227.156333832 + 240 = 12.843666168
x = 12.843666168

Simplifying
x = 12.843666168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {467.156333832, 12.843666168}

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