-0.15x^2+150x=11000

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Solution for -0.15x^2+150x=11000 equation: 


Simplifying
-0.15x2 + 150x = 11000

Reorder the terms:
150x + -0.15x2 = 11000

Solving
150x + -0.15x2 = 11000

Solving for variable 'x'.

Reorder the terms:
-11000 + 150x + -0.15x2 = 11000 + -11000

Combine like terms: 11000 + -11000 = 0
-11000 + 150x + -0.15x2 = 0

Begin completing the square.  Divide all terms by
-0.15 the coefficient of the squared term: 

Divide each side by '-0.15'.
73333.33333 + -1000x + x2 = 0

Move the constant term to the right:

Add '-73333.33333' to each side of the equation.
73333.33333 + -1000x + -73333.33333 + x2 = 0 + -73333.33333

Reorder the terms:
73333.33333 + -73333.33333 + -1000x + x2 = 0 + -73333.33333

Combine like terms: 73333.33333 + -73333.33333 = 0.00000
0.00000 + -1000x + x2 = 0 + -73333.33333
-1000x + x2 = 0 + -73333.33333

Combine like terms: 0 + -73333.33333 = -73333.33333
-1000x + x2 = -73333.33333

The x term is -1000x.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000x + 250000 + x2 = -73333.33333 + 250000

Reorder the terms:
250000 + -1000x + x2 = -73333.33333 + 250000

Combine like terms: -73333.33333 + 250000 = 176666.66667
250000 + -1000x + x2 = 176666.66667

Factor a perfect square on the left side:
(x + -500)(x + -500) = 176666.66667

Calculate the square root of the right side: 420.317340435

Break this problem into two subproblems by setting 
(x + -500) equal to 420.317340435 and -420.317340435.


Subproblem 1
x + -500 = 420.317340435

Simplifying
x + -500 = 420.317340435

Reorder the terms:
-500 + x = 420.317340435

Solving
-500 + x = 420.317340435

Solving for variable 'x'.

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

Add '500' to each side of the equation.
-500 + 500 + x = 420.317340435 + 500

Combine like terms: -500 + 500 = 0
0 + x = 420.317340435 + 500
x = 420.317340435 + 500

Combine like terms: 420.317340435 + 500 = 920.317340435
x = 920.317340435

Simplifying
x = 920.317340435


Subproblem 2
x + -500 = -420.317340435

Simplifying
x + -500 = -420.317340435

Reorder the terms:
-500 + x = -420.317340435

Solving
-500 + x = -420.317340435

Solving for variable 'x'.

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

Add '500' to each side of the equation.
-500 + 500 + x = -420.317340435 + 500

Combine like terms: -500 + 500 = 0
0 + x = -420.317340435 + 500
x = -420.317340435 + 500

Combine like terms: -420.317340435 + 500 = 79.682659565
x = 79.682659565

Simplifying
x = 79.682659565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {920.317340435, 79.682659565}

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