n^2-4=11n

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Solution for n^2-4=11n equation:


Simplifying
n2 + -4 = 11n

Reorder the terms:
-4 + n2 = 11n

Solving
-4 + n2 = 11n

Solving for variable 'n'.

Reorder the terms:
-4 + -11n + n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
-4 + -11n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -11n + 4 + n2 = 0 + 4

Reorder the terms:
-4 + 4 + -11n + n2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -11n + n2 = 0 + 4
-11n + n2 = 0 + 4

Combine like terms: 0 + 4 = 4
-11n + n2 = 4

The n term is -11n.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11n + 30.25 + n2 = 4 + 30.25

Reorder the terms:
30.25 + -11n + n2 = 4 + 30.25

Combine like terms: 4 + 30.25 = 34.25
30.25 + -11n + n2 = 34.25

Factor a perfect square on the left side:
(n + -5.5)(n + -5.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(n + -5.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

n + -5.5 = 5.852349955 Simplifying n + -5.5 = 5.852349955 Reorder the terms: -5.5 + n = 5.852349955 Solving -5.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 5.852349955 + 5.5 n = 5.852349955 + 5.5 Combine like terms: 5.852349955 + 5.5 = 11.352349955 n = 11.352349955 Simplifying n = 11.352349955

Subproblem 2

n + -5.5 = -5.852349955 Simplifying n + -5.5 = -5.852349955 Reorder the terms: -5.5 + n = -5.852349955 Solving -5.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -5.852349955 + 5.5 n = -5.852349955 + 5.5 Combine like terms: -5.852349955 + 5.5 = -0.352349955 n = -0.352349955 Simplifying n = -0.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.352349955, -0.352349955}

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