n^2-11n+30.25=0

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Solution for n^2-11n+30.25=0 equation:


Simplifying
n2 + -11n + 30.25 = 0

Reorder the terms:
30.25 + -11n + n2 = 0

Solving
30.25 + -11n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-30.25' to each side of the equation.
30.25 + -11n + -30.25 + n2 = 0 + -30.25

Reorder the terms:
30.25 + -30.25 + -11n + n2 = 0 + -30.25

Combine like terms: 30.25 + -30.25 = 0.00
0.00 + -11n + n2 = 0 + -30.25
-11n + n2 = 0 + -30.25

Combine like terms: 0 + -30.25 = -30.25
-11n + n2 = -30.25

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 = -30.25 + 30.25

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

Combine like terms: -30.25 + 30.25 = 0.00
30.25 + -11n + n2 = 0.00

Factor a perfect square on the left side:
(n + -5.5)(n + -5.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(n + -5.5) equal to 0.00 and 0.00.

Subproblem 1

n + -5.5 = 0.00 Simplifying n + -5.5 = 0.00 Reorder the terms: -5.5 + n = 0.00 Solving -5.5 + n = 0.00 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 = 0.00 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 0.00 + 5.5 n = 0.00 + 5.5 Combine like terms: 0.00 + 5.5 = 5.5 n = 5.5 Simplifying n = 5.5

Subproblem 2

n + -5.5 = 0.00 Simplifying n + -5.5 = 0.00 Reorder the terms: -5.5 + n = 0.00 Solving -5.5 + n = 0.00 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 = 0.00 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 0.00 + 5.5 n = 0.00 + 5.5 Combine like terms: 0.00 + 5.5 = 5.5 n = 5.5 Simplifying n = 5.5

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.5, 5.5}

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