n(17+5n)=900

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Solution for n(17+5n)=900 equation:


Simplifying
n(17 + 5n) = 900
(17 * n + 5n * n) = 900
(17n + 5n2) = 900

Solving
17n + 5n2 = 900

Solving for variable 'n'.

Reorder the terms:
-900 + 17n + 5n2 = 900 + -900

Combine like terms: 900 + -900 = 0
-900 + 17n + 5n2 = 0

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

Divide each side by '5'.
-180 + 3.4n + n2 = 0

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 3.4n + 180 + n2 = 0 + 180

Reorder the terms:
-180 + 180 + 3.4n + n2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 3.4n + n2 = 0 + 180
3.4n + n2 = 0 + 180

Combine like terms: 0 + 180 = 180
3.4n + n2 = 180

The n term is 3.4n.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4n + 2.89 + n2 = 180 + 2.89

Reorder the terms:
2.89 + 3.4n + n2 = 180 + 2.89

Combine like terms: 180 + 2.89 = 182.89
2.89 + 3.4n + n2 = 182.89

Factor a perfect square on the left side:
(n + 1.7)(n + 1.7) = 182.89

Calculate the square root of the right side: 13.52368293

Break this problem into two subproblems by setting 
(n + 1.7) equal to 13.52368293 and -13.52368293.

Subproblem 1

n + 1.7 = 13.52368293 Simplifying n + 1.7 = 13.52368293 Reorder the terms: 1.7 + n = 13.52368293 Solving 1.7 + n = 13.52368293 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + n = 13.52368293 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = 13.52368293 + -1.7 n = 13.52368293 + -1.7 Combine like terms: 13.52368293 + -1.7 = 11.82368293 n = 11.82368293 Simplifying n = 11.82368293

Subproblem 2

n + 1.7 = -13.52368293 Simplifying n + 1.7 = -13.52368293 Reorder the terms: 1.7 + n = -13.52368293 Solving 1.7 + n = -13.52368293 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + n = -13.52368293 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = -13.52368293 + -1.7 n = -13.52368293 + -1.7 Combine like terms: -13.52368293 + -1.7 = -15.22368293 n = -15.22368293 Simplifying n = -15.22368293

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.82368293, -15.22368293}

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