n^2+8n+3=0

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Solution for n^2+8n+3=0 equation:


Simplifying
n2 + 8n + 3 = 0

Reorder the terms:
3 + 8n + n2 = 0

Solving
3 + 8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + 8n + n2 = 0 + -3

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

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

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 = -3 + 16

Reorder the terms:
16 + 8n + n2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + 8n + n2 = 13

Factor a perfect square on the left side:
(n + 4)(n + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(n + 4) equal to 3.605551275 and -3.605551275.

Subproblem 1

n + 4 = 3.605551275 Simplifying n + 4 = 3.605551275 Reorder the terms: 4 + n = 3.605551275 Solving 4 + n = 3.605551275 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 = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + n = 3.605551275 + -4 n = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 n = -0.394448725 Simplifying n = -0.394448725

Subproblem 2

n + 4 = -3.605551275 Simplifying n + 4 = -3.605551275 Reorder the terms: 4 + n = -3.605551275 Solving 4 + n = -3.605551275 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 = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + n = -3.605551275 + -4 n = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 n = -7.605551275 Simplifying n = -7.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.394448725, -7.605551275}

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