200n^2+299n-2569000=0

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Solution for 200n^2+299n-2569000=0 equation:


Simplifying
200n2 + 299n + -2569000 = 0

Reorder the terms:
-2569000 + 299n + 200n2 = 0

Solving
-2569000 + 299n + 200n2 = 0

Solving for variable 'n'.

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

Divide each side by '200'.
-12845 + 1.495n + n2 = 0

Move the constant term to the right:

Add '12845' to each side of the equation.
-12845 + 1.495n + 12845 + n2 = 0 + 12845

Reorder the terms:
-12845 + 12845 + 1.495n + n2 = 0 + 12845

Combine like terms: -12845 + 12845 = 0
0 + 1.495n + n2 = 0 + 12845
1.495n + n2 = 0 + 12845

Combine like terms: 0 + 12845 = 12845
1.495n + n2 = 12845

The n term is 1.495n.  Take half its coefficient (0.7475).
Square it (0.55875625) and add it to both sides.

Add '0.55875625' to each side of the equation.
1.495n + 0.55875625 + n2 = 12845 + 0.55875625

Reorder the terms:
0.55875625 + 1.495n + n2 = 12845 + 0.55875625

Combine like terms: 12845 + 0.55875625 = 12845.55875625
0.55875625 + 1.495n + n2 = 12845.55875625

Factor a perfect square on the left side:
(n + 0.7475)(n + 0.7475) = 12845.55875625

Calculate the square root of the right side: 113.338249308

Break this problem into two subproblems by setting 
(n + 0.7475) equal to 113.338249308 and -113.338249308.

Subproblem 1

n + 0.7475 = 113.338249308 Simplifying n + 0.7475 = 113.338249308 Reorder the terms: 0.7475 + n = 113.338249308 Solving 0.7475 + n = 113.338249308 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.7475' to each side of the equation. 0.7475 + -0.7475 + n = 113.338249308 + -0.7475 Combine like terms: 0.7475 + -0.7475 = 0.0000 0.0000 + n = 113.338249308 + -0.7475 n = 113.338249308 + -0.7475 Combine like terms: 113.338249308 + -0.7475 = 112.590749308 n = 112.590749308 Simplifying n = 112.590749308

Subproblem 2

n + 0.7475 = -113.338249308 Simplifying n + 0.7475 = -113.338249308 Reorder the terms: 0.7475 + n = -113.338249308 Solving 0.7475 + n = -113.338249308 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.7475' to each side of the equation. 0.7475 + -0.7475 + n = -113.338249308 + -0.7475 Combine like terms: 0.7475 + -0.7475 = 0.0000 0.0000 + n = -113.338249308 + -0.7475 n = -113.338249308 + -0.7475 Combine like terms: -113.338249308 + -0.7475 = -114.085749308 n = -114.085749308 Simplifying n = -114.085749308

Solution

The solution to the problem is based on the solutions from the subproblems. n = {112.590749308, -114.085749308}

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