n^2+16n+42=8

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Solution for n^2+16n+42=8 equation:


Simplifying
n2 + 16n + 42 = 8

Reorder the terms:
42 + 16n + n2 = 8

Solving
42 + 16n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
42 + -8 + 16n + n2 = 8 + -8

Combine like terms: 42 + -8 = 34
34 + 16n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
34 + 16n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + 16n + -34 + n2 = 0 + -34

Reorder the terms:
34 + -34 + 16n + n2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + 16n + n2 = 0 + -34
16n + n2 = 0 + -34

Combine like terms: 0 + -34 = -34
16n + n2 = -34

The n term is 16n.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16n + 64 + n2 = -34 + 64

Reorder the terms:
64 + 16n + n2 = -34 + 64

Combine like terms: -34 + 64 = 30
64 + 16n + n2 = 30

Factor a perfect square on the left side:
(n + 8)(n + 8) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(n + 8) equal to 5.477225575 and -5.477225575.

Subproblem 1

n + 8 = 5.477225575 Simplifying n + 8 = 5.477225575 Reorder the terms: 8 + n = 5.477225575 Solving 8 + n = 5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + n = 5.477225575 + -8 n = 5.477225575 + -8 Combine like terms: 5.477225575 + -8 = -2.522774425 n = -2.522774425 Simplifying n = -2.522774425

Subproblem 2

n + 8 = -5.477225575 Simplifying n + 8 = -5.477225575 Reorder the terms: 8 + n = -5.477225575 Solving 8 + n = -5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = -5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + n = -5.477225575 + -8 n = -5.477225575 + -8 Combine like terms: -5.477225575 + -8 = -13.477225575 n = -13.477225575 Simplifying n = -13.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-2.522774425, -13.477225575}

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