-0.05x^2-468.5x+900000=0

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Solution for -0.05x^2-468.5x+900000=0 equation: 


Simplifying
-0.05x2 + -468.5x + 900000 = 0

Reorder the terms:
900000 + -468.5x + -0.05x2 = 0

Solving
900000 + -468.5x + -0.05x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-18000000 + 9370x + x2 = 0

Move the constant term to the right:

Add '18000000' to each side of the equation.
-18000000 + 9370x + 18000000 + x2 = 0 + 18000000

Reorder the terms:
-18000000 + 18000000 + 9370x + x2 = 0 + 18000000

Combine like terms: -18000000 + 18000000 = 0
0 + 9370x + x2 = 0 + 18000000
9370x + x2 = 0 + 18000000

Combine like terms: 0 + 18000000 = 18000000
9370x + x2 = 18000000

The x term is 9370x.  Take half its coefficient (4685).
Square it (21949225) and add it to both sides.

Add '21949225' to each side of the equation.
9370x + 21949225 + x2 = 18000000 + 21949225

Reorder the terms:
21949225 + 9370x + x2 = 18000000 + 21949225

Combine like terms: 18000000 + 21949225 = 39949225
21949225 + 9370x + x2 = 39949225

Factor a perfect square on the left side:
(x + 4685)(x + 4685) = 39949225

Calculate the square root of the right side: 6320.539929468

Break this problem into two subproblems by setting 
(x + 4685) equal to 6320.539929468 and -6320.539929468.


Subproblem 1
x + 4685 = 6320.539929468

Simplifying
x + 4685 = 6320.539929468

Reorder the terms:
4685 + x = 6320.539929468

Solving
4685 + x = 6320.539929468

Solving for variable 'x'.

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

Add '-4685' to each side of the equation.
4685 + -4685 + x = 6320.539929468 + -4685

Combine like terms: 4685 + -4685 = 0
0 + x = 6320.539929468 + -4685
x = 6320.539929468 + -4685

Combine like terms: 6320.539929468 + -4685 = 1635.539929468
x = 1635.539929468

Simplifying
x = 1635.539929468


Subproblem 2
x + 4685 = -6320.539929468

Simplifying
x + 4685 = -6320.539929468

Reorder the terms:
4685 + x = -6320.539929468

Solving
4685 + x = -6320.539929468

Solving for variable 'x'.

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

Add '-4685' to each side of the equation.
4685 + -4685 + x = -6320.539929468 + -4685

Combine like terms: 4685 + -4685 = 0
0 + x = -6320.539929468 + -4685
x = -6320.539929468 + -4685

Combine like terms: -6320.539929468 + -4685 = -11005.539929468
x = -11005.539929468

Simplifying
x = -11005.539929468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1635.539929468, -11005.539929468}

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