68-4n=n*n

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Solution for 68-4n=n*n equation:


Simplifying
68 + -4n = n * n

Multiply n * n
68 + -4n = n2

Solving
68 + -4n = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
68 + -4n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-68 + 4n + n2 = 0

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 4n + 68 + n2 = 0 + 68

Reorder the terms:
-68 + 68 + 4n + n2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 4n + n2 = 0 + 68
4n + n2 = 0 + 68

Combine like terms: 0 + 68 = 68
4n + n2 = 68

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = 68 + 4

Reorder the terms:
4 + 4n + n2 = 68 + 4

Combine like terms: 68 + 4 = 72
4 + 4n + n2 = 72

Factor a perfect square on the left side:
(n + 2)(n + 2) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(n + 2) equal to 8.485281374 and -8.485281374.

Subproblem 1

n + 2 = 8.485281374 Simplifying n + 2 = 8.485281374 Reorder the terms: 2 + n = 8.485281374 Solving 2 + n = 8.485281374 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 8.485281374 + -2 Combine like terms: 2 + -2 = 0 0 + n = 8.485281374 + -2 n = 8.485281374 + -2 Combine like terms: 8.485281374 + -2 = 6.485281374 n = 6.485281374 Simplifying n = 6.485281374

Subproblem 2

n + 2 = -8.485281374 Simplifying n + 2 = -8.485281374 Reorder the terms: 2 + n = -8.485281374 Solving 2 + n = -8.485281374 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -8.485281374 + -2 Combine like terms: 2 + -2 = 0 0 + n = -8.485281374 + -2 n = -8.485281374 + -2 Combine like terms: -8.485281374 + -2 = -10.485281374 n = -10.485281374 Simplifying n = -10.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.485281374, -10.485281374}

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