2n^2-13n+5=0

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Solution for 2n^2-13n+5=0 equation:


Simplifying
2n2 + -13n + 5 = 0

Reorder the terms:
5 + -13n + 2n2 = 0

Solving
5 + -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'.
2.5 + -6.5n + n2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6.5n + -2.5 + n2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6.5n + n2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6.5n + n2 = 0 + -2.5
-6.5n + n2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6.5n + n2 = -2.5

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 = -2.5 + 10.5625

Reorder the terms:
10.5625 + -6.5n + n2 = -2.5 + 10.5625

Combine like terms: -2.5 + 10.5625 = 8.0625
10.5625 + -6.5n + n2 = 8.0625

Factor a perfect square on the left side:
(n + -3.25)(n + -3.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(n + -3.25) equal to 2.839454173 and -2.839454173.

Subproblem 1

n + -3.25 = 2.839454173 Simplifying n + -3.25 = 2.839454173 Reorder the terms: -3.25 + n = 2.839454173 Solving -3.25 + n = 2.839454173 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 = 2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 2.839454173 + 3.25 n = 2.839454173 + 3.25 Combine like terms: 2.839454173 + 3.25 = 6.089454173 n = 6.089454173 Simplifying n = 6.089454173

Subproblem 2

n + -3.25 = -2.839454173 Simplifying n + -3.25 = -2.839454173 Reorder the terms: -3.25 + n = -2.839454173 Solving -3.25 + n = -2.839454173 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 = -2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -2.839454173 + 3.25 n = -2.839454173 + 3.25 Combine like terms: -2.839454173 + 3.25 = 0.410545827 n = 0.410545827 Simplifying n = 0.410545827

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.089454173, 0.410545827}

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