2n^2+n-14=0

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Solution for 2n^2+n-14=0 equation:


Simplifying
2n2 + n + -14 = 0

Reorder the terms:
-14 + n + 2n2 = 0

Solving
-14 + n + 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'.
-7 + 0.5n + n2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 0.5n + 7 + n2 = 0 + 7

Reorder the terms:
-7 + 7 + 0.5n + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 0.5n + n2 = 0 + 7
0.5n + n2 = 0 + 7

Combine like terms: 0 + 7 = 7
0.5n + n2 = 7

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5n + 0.25 + n2 = 7 + 0.25

Reorder the terms:
0.25 + 0.5n + n2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + 0.5n + n2 = 7.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(n + 0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

n + 0.5 = 2.692582404 Simplifying n + 0.5 = 2.692582404 Reorder the terms: 0.5 + n = 2.692582404 Solving 0.5 + n = 2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 2.692582404 + -0.5 n = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 n = 2.192582404 Simplifying n = 2.192582404

Subproblem 2

n + 0.5 = -2.692582404 Simplifying n + 0.5 = -2.692582404 Reorder the terms: 0.5 + n = -2.692582404 Solving 0.5 + n = -2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -2.692582404 + -0.5 n = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 n = -3.192582404 Simplifying n = -3.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.192582404, -3.192582404}

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