-5-n(1+7n)=-8

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Solution for -5-n(1+7n)=-8 equation:


Simplifying
-5 + -1n(1 + 7n) = -8
-5 + (1 * -1n + 7n * -1n) = -8
-5 + (-1n + -7n2) = -8

Solving
-5 + -1n + -7n2 = -8

Solving for variable 'n'.

Reorder the terms:
-5 + 8 + -1n + -7n2 = -8 + 8

Combine like terms: -5 + 8 = 3
3 + -1n + -7n2 = -8 + 8

Combine like terms: -8 + 8 = 0
3 + -1n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.4285714286 + 0.1428571429n + n2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.1428571429n + 0.4285714286 + n2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.1428571429n + n2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.1428571429n + n2 = 0 + 0.4285714286
0.1428571429n + n2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.1428571429n + n2 = 0.4285714286

The n term is 0.1428571429n.  Take half its coefficient (0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
0.1428571429n + 0.005102040819 + n2 = 0.4285714286 + 0.005102040819

Reorder the terms:
0.005102040819 + 0.1428571429n + n2 = 0.4285714286 + 0.005102040819

Combine like terms: 0.4285714286 + 0.005102040819 = 0.433673469419
0.005102040819 + 0.1428571429n + n2 = 0.433673469419

Factor a perfect square on the left side:
(n + 0.07142857145)(n + 0.07142857145) = 0.433673469419

Calculate the square root of the right side: 0.65853889

Break this problem into two subproblems by setting 
(n + 0.07142857145) equal to 0.65853889 and -0.65853889.

Subproblem 1

n + 0.07142857145 = 0.65853889 Simplifying n + 0.07142857145 = 0.65853889 Reorder the terms: 0.07142857145 + n = 0.65853889 Solving 0.07142857145 + n = 0.65853889 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + n = 0.65853889 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + n = 0.65853889 + -0.07142857145 n = 0.65853889 + -0.07142857145 Combine like terms: 0.65853889 + -0.07142857145 = 0.58711031855 n = 0.58711031855 Simplifying n = 0.58711031855

Subproblem 2

n + 0.07142857145 = -0.65853889 Simplifying n + 0.07142857145 = -0.65853889 Reorder the terms: 0.07142857145 + n = -0.65853889 Solving 0.07142857145 + n = -0.65853889 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + n = -0.65853889 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + n = -0.65853889 + -0.07142857145 n = -0.65853889 + -0.07142857145 Combine like terms: -0.65853889 + -0.07142857145 = -0.72996746145 n = -0.72996746145 Simplifying n = -0.72996746145

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.58711031855, -0.72996746145}

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