2n^2-13n+7=0

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Solution for 2n^2-13n+7=0 equation:


Simplifying
2n2 + -13n + 7 = 0

Reorder the terms:
7 + -13n + 2n2 = 0

Solving
7 + -13n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
3.5 + -6.5n + n2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -6.5n + -3.5 + n2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -6.5n + n2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -6.5n + n2 = 0 + -3.5
-6.5n + n2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-6.5n + n2 = -3.5

The n term is -6.5n.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5n + 10.5625 + n2 = -3.5 + 10.5625

Reorder the terms:
10.5625 + -6.5n + n2 = -3.5 + 10.5625

Combine like terms: -3.5 + 10.5625 = 7.0625
10.5625 + -6.5n + n2 = 7.0625

Factor a perfect square on the left side:
(n + -3.25)(n + -3.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(n + -3.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

n + -3.25 = 2.657536453 Simplifying n + -3.25 = 2.657536453 Reorder the terms: -3.25 + n = 2.657536453 Solving -3.25 + n = 2.657536453 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = 2.657536453 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 2.657536453 + 3.25 n = 2.657536453 + 3.25 Combine like terms: 2.657536453 + 3.25 = 5.907536453 n = 5.907536453 Simplifying n = 5.907536453

Subproblem 2

n + -3.25 = -2.657536453 Simplifying n + -3.25 = -2.657536453 Reorder the terms: -3.25 + n = -2.657536453 Solving -3.25 + n = -2.657536453 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = -2.657536453 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -2.657536453 + 3.25 n = -2.657536453 + 3.25 Combine like terms: -2.657536453 + 3.25 = 0.592463547 n = 0.592463547 Simplifying n = 0.592463547

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.907536453, 0.592463547}

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