557x-0.5x^2=139460

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Solution for 557x-0.5x^2=139460 equation: 


Simplifying
557x + -0.5x2 = 139460

Solving
557x + -0.5x2 = 139460

Solving for variable 'x'.

Reorder the terms:
-139460 + 557x + -0.5x2 = 139460 + -139460

Combine like terms: 139460 + -139460 = 0
-139460 + 557x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
278920 + -1114x + x2 = 0

Move the constant term to the right:

Add '-278920' to each side of the equation.
278920 + -1114x + -278920 + x2 = 0 + -278920

Reorder the terms:
278920 + -278920 + -1114x + x2 = 0 + -278920

Combine like terms: 278920 + -278920 = 0
0 + -1114x + x2 = 0 + -278920
-1114x + x2 = 0 + -278920

Combine like terms: 0 + -278920 = -278920
-1114x + x2 = -278920

The x term is -1114x.  Take half its coefficient (-557).
Square it (310249) and add it to both sides.

Add '310249' to each side of the equation.
-1114x + 310249 + x2 = -278920 + 310249

Reorder the terms:
310249 + -1114x + x2 = -278920 + 310249

Combine like terms: -278920 + 310249 = 31329
310249 + -1114x + x2 = 31329

Factor a perfect square on the left side:
(x + -557)(x + -557) = 31329

Calculate the square root of the right side: 177

Break this problem into two subproblems by setting 
(x + -557) equal to 177 and -177.


Subproblem 1
x + -557 = 177

Simplifying
x + -557 = 177

Reorder the terms:
-557 + x = 177

Solving
-557 + x = 177

Solving for variable 'x'.

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

Add '557' to each side of the equation.
-557 + 557 + x = 177 + 557

Combine like terms: -557 + 557 = 0
0 + x = 177 + 557
x = 177 + 557

Combine like terms: 177 + 557 = 734
x = 734

Simplifying
x = 734


Subproblem 2
x + -557 = -177

Simplifying
x + -557 = -177

Reorder the terms:
-557 + x = -177

Solving
-557 + x = -177

Solving for variable 'x'.

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

Add '557' to each side of the equation.
-557 + 557 + x = -177 + 557

Combine like terms: -557 + 557 = 0
0 + x = -177 + 557
x = -177 + 557

Combine like terms: -177 + 557 = 380
x = 380

Simplifying
x = 380


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {734, 380}

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