-x^2+208x+5000=0

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Solution for -x^2+208x+5000=0 equation:


Simplifying
-1x2 + 208x + 5000 = 0

Reorder the terms:
5000 + 208x + -1x2 = 0

Solving
5000 + 208x + -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'.
-5000 + -208x + x2 = 0

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + -208x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + -208x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + -208x + x2 = 0 + 5000
-208x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
-208x + x2 = 5000

The x term is -208x.  Take half its coefficient (-104).
Square it (10816) and add it to both sides.

Add '10816' to each side of the equation.
-208x + 10816 + x2 = 5000 + 10816

Reorder the terms:
10816 + -208x + x2 = 5000 + 10816

Combine like terms: 5000 + 10816 = 15816
10816 + -208x + x2 = 15816

Factor a perfect square on the left side:
(x + -104)(x + -104) = 15816

Calculate the square root of the right side: 125.761679378

Break this problem into two subproblems by setting 
(x + -104) equal to 125.761679378 and -125.761679378.

Subproblem 1

x + -104 = 125.761679378 Simplifying x + -104 = 125.761679378 Reorder the terms: -104 + x = 125.761679378 Solving -104 + x = 125.761679378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104' to each side of the equation. -104 + 104 + x = 125.761679378 + 104 Combine like terms: -104 + 104 = 0 0 + x = 125.761679378 + 104 x = 125.761679378 + 104 Combine like terms: 125.761679378 + 104 = 229.761679378 x = 229.761679378 Simplifying x = 229.761679378

Subproblem 2

x + -104 = -125.761679378 Simplifying x + -104 = -125.761679378 Reorder the terms: -104 + x = -125.761679378 Solving -104 + x = -125.761679378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104' to each side of the equation. -104 + 104 + x = -125.761679378 + 104 Combine like terms: -104 + 104 = 0 0 + x = -125.761679378 + 104 x = -125.761679378 + 104 Combine like terms: -125.761679378 + 104 = -21.761679378 x = -21.761679378 Simplifying x = -21.761679378

Solution

The solution to the problem is based on the solutions from the subproblems. x = {229.761679378, -21.761679378}

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