11*(8-n)n=4

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Solution for 11*(8-n)n=4 equation:


Simplifying
11(8 + -1n) * n = 4

Reorder the terms for easier multiplication:
11n(8 + -1n) = 4
(8 * 11n + -1n * 11n) = 4
(88n + -11n2) = 4

Solving
88n + -11n2 = 4

Solving for variable 'n'.

Reorder the terms:
-4 + 88n + -11n2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 88n + -11n2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
0.3636363636 + -8n + n2 = 0

Move the constant term to the right:

Add '-0.3636363636' to each side of the equation.
0.3636363636 + -8n + -0.3636363636 + n2 = 0 + -0.3636363636

Reorder the terms:
0.3636363636 + -0.3636363636 + -8n + n2 = 0 + -0.3636363636

Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000
0.0000000000 + -8n + n2 = 0 + -0.3636363636
-8n + n2 = 0 + -0.3636363636

Combine like terms: 0 + -0.3636363636 = -0.3636363636
-8n + n2 = -0.3636363636

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = -0.3636363636 + 16

Reorder the terms:
16 + -8n + n2 = -0.3636363636 + 16

Combine like terms: -0.3636363636 + 16 = 15.6363636364
16 + -8n + n2 = 15.6363636364

Factor a perfect square on the left side:
(n + -4)(n + -4) = 15.6363636364

Calculate the square root of the right side: 3.954284213

Break this problem into two subproblems by setting 
(n + -4) equal to 3.954284213 and -3.954284213.

Subproblem 1

n + -4 = 3.954284213 Simplifying n + -4 = 3.954284213 Reorder the terms: -4 + n = 3.954284213 Solving -4 + n = 3.954284213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 3.954284213 + 4 Combine like terms: -4 + 4 = 0 0 + n = 3.954284213 + 4 n = 3.954284213 + 4 Combine like terms: 3.954284213 + 4 = 7.954284213 n = 7.954284213 Simplifying n = 7.954284213

Subproblem 2

n + -4 = -3.954284213 Simplifying n + -4 = -3.954284213 Reorder the terms: -4 + n = -3.954284213 Solving -4 + n = -3.954284213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -3.954284213 + 4 Combine like terms: -4 + 4 = 0 0 + n = -3.954284213 + 4 n = -3.954284213 + 4 Combine like terms: -3.954284213 + 4 = 0.045715787 n = 0.045715787 Simplifying n = 0.045715787

Solution

The solution to the problem is based on the solutions from the subproblems. n = {7.954284213, 0.045715787}

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