x(10-x)=-250

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Solution for x(10-x)=-250 equation:


Simplifying
x(10 + -1x) = -250
(10 * x + -1x * x) = -250
(10x + -1x2) = -250

Solving
10x + -1x2 = -250

Solving for variable 'x'.

Reorder the terms:
250 + 10x + -1x2 = -250 + 250

Combine like terms: -250 + 250 = 0
250 + 10x + -1x2 = 0

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

Divide each side by '-1'.
-250 + -10x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -10x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -10x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -10x + x2 = 0 + 250
-10x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-10x + x2 = 250

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 250 + 25

Reorder the terms:
25 + -10x + x2 = 250 + 25

Combine like terms: 250 + 25 = 275
25 + -10x + x2 = 275

Factor a perfect square on the left side:
(x + -5)(x + -5) = 275

Calculate the square root of the right side: 16.583123952

Break this problem into two subproblems by setting 
(x + -5) equal to 16.583123952 and -16.583123952.

Subproblem 1

x + -5 = 16.583123952 Simplifying x + -5 = 16.583123952 Reorder the terms: -5 + x = 16.583123952 Solving -5 + x = 16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 16.583123952 + 5 Combine like terms: -5 + 5 = 0 0 + x = 16.583123952 + 5 x = 16.583123952 + 5 Combine like terms: 16.583123952 + 5 = 21.583123952 x = 21.583123952 Simplifying x = 21.583123952

Subproblem 2

x + -5 = -16.583123952 Simplifying x + -5 = -16.583123952 Reorder the terms: -5 + x = -16.583123952 Solving -5 + x = -16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -16.583123952 + 5 Combine like terms: -5 + 5 = 0 0 + x = -16.583123952 + 5 x = -16.583123952 + 5 Combine like terms: -16.583123952 + 5 = -11.583123952 x = -11.583123952 Simplifying x = -11.583123952

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.583123952, -11.583123952}

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