5n^2-44n=6n-21

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Solution for 5n^2-44n=6n-21 equation:


Simplifying
5n2 + -44n = 6n + -21

Reorder the terms:
-44n + 5n2 = 6n + -21

Reorder the terms:
-44n + 5n2 = -21 + 6n

Solving
-44n + 5n2 = -21 + 6n

Solving for variable 'n'.

Reorder the terms:
21 + -44n + -6n + 5n2 = -21 + 6n + 21 + -6n

Combine like terms: -44n + -6n = -50n
21 + -50n + 5n2 = -21 + 6n + 21 + -6n

Reorder the terms:
21 + -50n + 5n2 = -21 + 21 + 6n + -6n

Combine like terms: -21 + 21 = 0
21 + -50n + 5n2 = 0 + 6n + -6n
21 + -50n + 5n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
21 + -50n + 5n2 = 0

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

Divide each side by '5'.
4.2 + -10n + n2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + -10n + -4.2 + n2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + -10n + n2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + -10n + n2 = 0 + -4.2
-10n + n2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
-10n + n2 = -4.2

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = -4.2 + 25

Reorder the terms:
25 + -10n + n2 = -4.2 + 25

Combine like terms: -4.2 + 25 = 20.8
25 + -10n + n2 = 20.8

Factor a perfect square on the left side:
(n + -5)(n + -5) = 20.8

Calculate the square root of the right side: 4.5607017

Break this problem into two subproblems by setting 
(n + -5) equal to 4.5607017 and -4.5607017.

Subproblem 1

n + -5 = 4.5607017 Simplifying n + -5 = 4.5607017 Reorder the terms: -5 + n = 4.5607017 Solving -5 + n = 4.5607017 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 4.5607017 + 5 Combine like terms: -5 + 5 = 0 0 + n = 4.5607017 + 5 n = 4.5607017 + 5 Combine like terms: 4.5607017 + 5 = 9.5607017 n = 9.5607017 Simplifying n = 9.5607017

Subproblem 2

n + -5 = -4.5607017 Simplifying n + -5 = -4.5607017 Reorder the terms: -5 + n = -4.5607017 Solving -5 + n = -4.5607017 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -4.5607017 + 5 Combine like terms: -5 + 5 = 0 0 + n = -4.5607017 + 5 n = -4.5607017 + 5 Combine like terms: -4.5607017 + 5 = 0.4392983 n = 0.4392983 Simplifying n = 0.4392983

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.5607017, 0.4392983}

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