-x^2+20x+60000=0

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Solution for -x^2+20x+60000=0 equation: 


Simplifying
-1x2 + 20x + 60000 = 0

Reorder the terms:
60000 + 20x + -1x2 = 0

Solving
60000 + 20x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-60000 + -20x + x2 = 0

Move the constant term to the right:

Add '60000' to each side of the equation.
-60000 + -20x + 60000 + x2 = 0 + 60000

Reorder the terms:
-60000 + 60000 + -20x + x2 = 0 + 60000

Combine like terms: -60000 + 60000 = 0
0 + -20x + x2 = 0 + 60000
-20x + x2 = 0 + 60000

Combine like terms: 0 + 60000 = 60000
-20x + x2 = 60000

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 60000 + 100

Reorder the terms:
100 + -20x + x2 = 60000 + 100

Combine like terms: 60000 + 100 = 60100
100 + -20x + x2 = 60100

Factor a perfect square on the left side:
(x + -10)(x + -10) = 60100

Calculate the square root of the right side: 245.153013443

Break this problem into two subproblems by setting 
(x + -10) equal to 245.153013443 and -245.153013443.


Subproblem 1
x + -10 = 245.153013443

Simplifying
x + -10 = 245.153013443

Reorder the terms:
-10 + x = 245.153013443

Solving
-10 + x = 245.153013443

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 245.153013443 + 10

Combine like terms: -10 + 10 = 0
0 + x = 245.153013443 + 10
x = 245.153013443 + 10

Combine like terms: 245.153013443 + 10 = 255.153013443
x = 255.153013443

Simplifying
x = 255.153013443


Subproblem 2
x + -10 = -245.153013443

Simplifying
x + -10 = -245.153013443

Reorder the terms:
-10 + x = -245.153013443

Solving
-10 + x = -245.153013443

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -245.153013443 + 10

Combine like terms: -10 + 10 = 0
0 + x = -245.153013443 + 10
x = -245.153013443 + 10

Combine like terms: -245.153013443 + 10 = -235.153013443
x = -235.153013443

Simplifying
x = -235.153013443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {255.153013443, -235.153013443}

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