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# Calculator Output

```Simplifying
2n2 + -22n + 60 = 0

Reorder the terms:
60 + -22n + 2n2 = 0

Solving
60 + -22n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11n + n2) = 0

Ignore the factor 2.
Subproblem 1Set the factor '(30 + -11n + n2)' equal to zero and attempt to solve:

Simplifying
30 + -11n + n2 = 0

Solving
30 + -11n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -11n + -30 + n2 = 0 + -30

Reorder the terms:
30 + -30 + -11n + n2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -11n + n2 = 0 + -30
-11n + n2 = 0 + -30

Combine like terms: 0 + -30 = -30
-11n + n2 = -30

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 + 30.25

Reorder the terms:
30.25 + -11n + n2 = -30 + 30.25

Combine like terms: -30 + 30.25 = 0.25
30.25 + -11n + n2 = 0.25

Factor a perfect square on the left side:
(n + -5.5)(n + -5.5) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting
(n + -5.5) equal to 0.5 and -0.5.

Subproblem 1n + -5.5 = 0.5

Simplifying
n + -5.5 = 0.5

Reorder the terms:
-5.5 + n = 0.5

Solving
-5.5 + n = 0.5

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 = 0.5 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + n = 0.5 + 5.5
n = 0.5 + 5.5

Combine like terms: 0.5 + 5.5 = 6
n = 6

Simplifying
n = 6

Subproblem 2n + -5.5 = -0.5

Simplifying
n + -5.5 = -0.5

Reorder the terms:
-5.5 + n = -0.5

Solving
-5.5 + n = -0.5

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 = -0.5 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + n = -0.5 + 5.5
n = -0.5 + 5.5

Combine like terms: -0.5 + 5.5 = 5
n = 5

Simplifying
n = 5

SolutionThe solution to the problem is based on the solutions
from the subproblems.
n = {6, 5}Solutionn = {6, 5}```
Processing time: 1 ms. 76640644 equations since February 08, 2004.   Disclaimer

# Completing the Square Calculator

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