7n^2+43n-7600=0

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Solution for 7n^2+43n-7600=0 equation:


Simplifying
7n2 + 43n + -7600 = 0

Reorder the terms:
-7600 + 43n + 7n2 = 0

Solving
-7600 + 43n + 7n2 = 0

Solving for variable 'n'.

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

Divide each side by '7'.
-1085.714286 + 6.142857143n + n2 = 0

Move the constant term to the right:

Add '1085.714286' to each side of the equation.
-1085.714286 + 6.142857143n + 1085.714286 + n2 = 0 + 1085.714286

Reorder the terms:
-1085.714286 + 1085.714286 + 6.142857143n + n2 = 0 + 1085.714286

Combine like terms: -1085.714286 + 1085.714286 = 0.000000
0.000000 + 6.142857143n + n2 = 0 + 1085.714286
6.142857143n + n2 = 0 + 1085.714286

Combine like terms: 0 + 1085.714286 = 1085.714286
6.142857143n + n2 = 1085.714286

The n term is 6.142857143n.  Take half its coefficient (3.071428572).
Square it (9.433673473) and add it to both sides.

Add '9.433673473' to each side of the equation.
6.142857143n + 9.433673473 + n2 = 1085.714286 + 9.433673473

Reorder the terms:
9.433673473 + 6.142857143n + n2 = 1085.714286 + 9.433673473

Combine like terms: 1085.714286 + 9.433673473 = 1095.147959473
9.433673473 + 6.142857143n + n2 = 1095.147959473

Factor a perfect square on the left side:
(n + 3.071428572)(n + 3.071428572) = 1095.147959473

Calculate the square root of the right side: 33.0930198

Break this problem into two subproblems by setting 
(n + 3.071428572) equal to 33.0930198 and -33.0930198.

Subproblem 1

n + 3.071428572 = 33.0930198 Simplifying n + 3.071428572 = 33.0930198 Reorder the terms: 3.071428572 + n = 33.0930198 Solving 3.071428572 + n = 33.0930198 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + n = 33.0930198 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + n = 33.0930198 + -3.071428572 n = 33.0930198 + -3.071428572 Combine like terms: 33.0930198 + -3.071428572 = 30.021591228 n = 30.021591228 Simplifying n = 30.021591228

Subproblem 2

n + 3.071428572 = -33.0930198 Simplifying n + 3.071428572 = -33.0930198 Reorder the terms: 3.071428572 + n = -33.0930198 Solving 3.071428572 + n = -33.0930198 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + n = -33.0930198 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + n = -33.0930198 + -3.071428572 n = -33.0930198 + -3.071428572 Combine like terms: -33.0930198 + -3.071428572 = -36.164448372 n = -36.164448372 Simplifying n = -36.164448372

Solution

The solution to the problem is based on the solutions from the subproblems. n = {30.021591228, -36.164448372}

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