2n^2-11n+13=0

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Solution for 2n^2-11n+13=0 equation:


Simplifying
2n2 + -11n + 13 = 0

Reorder the terms:
13 + -11n + 2n2 = 0

Solving
13 + -11n + 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'.
6.5 + -5.5n + n2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -5.5n + -6.5 + n2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -5.5n + n2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -5.5n + n2 = 0 + -6.5
-5.5n + n2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-5.5n + n2 = -6.5

The n term is -5.5n.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5n + 7.5625 + n2 = -6.5 + 7.5625

Reorder the terms:
7.5625 + -5.5n + n2 = -6.5 + 7.5625

Combine like terms: -6.5 + 7.5625 = 1.0625
7.5625 + -5.5n + n2 = 1.0625

Factor a perfect square on the left side:
(n + -2.75)(n + -2.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(n + -2.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

n + -2.75 = 1.030776406 Simplifying n + -2.75 = 1.030776406 Reorder the terms: -2.75 + n = 1.030776406 Solving -2.75 + n = 1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = 1.030776406 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = 1.030776406 + 2.75 n = 1.030776406 + 2.75 Combine like terms: 1.030776406 + 2.75 = 3.780776406 n = 3.780776406 Simplifying n = 3.780776406

Subproblem 2

n + -2.75 = -1.030776406 Simplifying n + -2.75 = -1.030776406 Reorder the terms: -2.75 + n = -1.030776406 Solving -2.75 + n = -1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = -1.030776406 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = -1.030776406 + 2.75 n = -1.030776406 + 2.75 Combine like terms: -1.030776406 + 2.75 = 1.719223594 n = 1.719223594 Simplifying n = 1.719223594

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.780776406, 1.719223594}

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