2000000=-5x^2+15000x

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Solution for 2000000=-5x^2+15000x equation: 


Simplifying
2000000 = -5x2 + 15000x

Reorder the terms:
2000000 = 15000x + -5x2

Solving
2000000 = 15000x + -5x2

Solving for variable 'x'.

Reorder the terms:
2000000 + -15000x + 5x2 = 15000x + -15000x + -5x2 + 5x2

Combine like terms: 15000x + -15000x = 0
2000000 + -15000x + 5x2 = 0 + -5x2 + 5x2
2000000 + -15000x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
2000000 + -15000x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(400000 + -3000x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(400000 + -3000x + x2)' equal to zero and attempt to solve:

Simplifying
400000 + -3000x + x2 = 0

Solving
400000 + -3000x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-400000' to each side of the equation.
400000 + -3000x + -400000 + x2 = 0 + -400000

Reorder the terms:
400000 + -400000 + -3000x + x2 = 0 + -400000

Combine like terms: 400000 + -400000 = 0
0 + -3000x + x2 = 0 + -400000
-3000x + x2 = 0 + -400000

Combine like terms: 0 + -400000 = -400000
-3000x + x2 = -400000

The x term is -3000x.  Take half its coefficient (-1500).
Square it (2250000) and add it to both sides.

Add '2250000' to each side of the equation.
-3000x + 2250000 + x2 = -400000 + 2250000

Reorder the terms:
2250000 + -3000x + x2 = -400000 + 2250000

Combine like terms: -400000 + 2250000 = 1850000
2250000 + -3000x + x2 = 1850000

Factor a perfect square on the left side:
(x + -1500)(x + -1500) = 1850000

Calculate the square root of the right side: 1360.147050874

Break this problem into two subproblems by setting 
(x + -1500) equal to 1360.147050874 and -1360.147050874.


Subproblem 1
x + -1500 = 1360.147050874

Simplifying
x + -1500 = 1360.147050874

Reorder the terms:
-1500 + x = 1360.147050874

Solving
-1500 + x = 1360.147050874

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = 1360.147050874 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = 1360.147050874 + 1500
x = 1360.147050874 + 1500

Combine like terms: 1360.147050874 + 1500 = 2860.147050874
x = 2860.147050874

Simplifying
x = 2860.147050874


Subproblem 2
x + -1500 = -1360.147050874

Simplifying
x + -1500 = -1360.147050874

Reorder the terms:
-1500 + x = -1360.147050874

Solving
-1500 + x = -1360.147050874

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = -1360.147050874 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = -1360.147050874 + 1500
x = -1360.147050874 + 1500

Combine like terms: -1360.147050874 + 1500 = 139.852949126
x = 139.852949126

Simplifying
x = 139.852949126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2860.147050874, 139.852949126}
Solution
x = {2860.147050874, 139.852949126}

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